Luxembourg - Math Olympiad Question | You should know this trick
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- Опубликовано: 29 сен 2024
- Maths Olympiads are held all around the world to recognise students who excel in maths. The test is offered at many grade levels and provides them with numerous possibilities to win certifications, awards, and even scholarships for higher studies.
It is too simple for Math-Olympiad.
Agreed
No
@@furina9053Olympiad math is just a whole different level man, thats why they mentioned it
I think it was maybe paralympic games
Maybe it was from the qualifier level exam
People commenting it is too simple are unrecognized genius. I wonder why they are wasting their time watching youtube videos. I mean, it is not the hardest question, but it does takes more thinking than a regular polynomial question and corresponds to high school students level
Skill issue 😂
Ha ha
So funny man.
You probably should become a standing comedian@@dhonikumarshahi2806
Please give any practical use of learning this?
Your just doing the math there’s no explaination along the way.
It can be root 2 -1 or 1-root 2
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I am a genuine maths dunce. Don't remember learning any of this and I don't understand it now either! 😅
Every one has their own unique talent sir....
Bro are you from America 😂
@@Ispeakwithlogicif you think Americans are dumb you should see which country has the most medals in International Math Olympiad
Nice trick
As a martian, I teached myself this trick at 6 months old, by observing shadow patterns in our red planet.
😂
Ain't no martian looks like a mongoose 🗣️
We were solving such problems in my 8th grade in Romania in a regular maths class. Too simple for an Olympiad.
no one cares
I'm sure third world Romania isn't.
I wonder if no baddy needs mathema😊ticks why still teach them
Cope and seethe.
China and Romania have always been at the top when in comes to math, but I don't necessarily think the method used to achieve that goal was a positive one.
One should be careful in distinguishing between 'equals' and 'implies' symbols.
Instead of looking for (a-b)^2 = 3 - 2 sqrt(2), I looked for (a + b sqrt(2))^2 = (3 - 2 sqrt(2)), with a, b rational numbers. The advantage here is that I don't have to pull a and b out of thin air: I can solve for them.
In this case we have a^2 + 2 b^2 = 3 and 2ab = -2. There are two solutions here: a = -1, b = 1, and a = 1, b = -1. The latter choice is the positive result implied by the radical. So the answer is -1 + sqrt(2).
How did I know to look for an answer in this form? From more advanced math, I know that Q[sqrt(2)] is a field, which means specifically for us that it's closed under multiplication. So it's a good place to start when looking for roots of a polynomial.
Lies again? Must See TV Deaf Blind
I remember seeing this trick of manipulation of sqrt(2) like imaginary numbers, but I didn’t realize it had a formal name Q(sqrt(2))
You can also use the fact that for a = sqrt(3 - sqrt(8)) and b = sqrt(3 + sqrt(8)) we find that ab = 1 and a + b = sqrt(8), hence x^2 - sqrt(8)x + 1 = 0 have - 1 + sqrt(2) and 1 + sqrt(2) for solution.
So -1 is on of your answers for a square root problem? What times what equals negative 1?
Ooops...
2+2= 4
People saying this is too simple, and while it kind of is simple, it is also hard to come up with unless you are trained to apply this kind of thinking in problems. I would have never guessed to use the square of difference identity, feels like its a problem you have to be familiar with beforehand
Yupp, one must have known the patterns before
I think its not that hard. In √(3-2√2), the 3-2√2 is inside a sq root, which makes us try forms like (a±b)^2
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
"it is also hard to come up with unless you are trained to apply this kind of thinking in problems"
.
those who are spesicically trained for olympiands, will be trained for this and much more , becomes it too easy for them.
@mar2506 an averag 8th grader from India will be able to this in seconds brh.
U'll find this in cbse books
Sadly I was totally confused. She showed us a rather lengthy process, but with ABSOLUTELY NO explanation for why we are doing all these arcane steps. I think this is probably the worst possible explanation of how to achieve the objective, because she showed us WHAT to do but with no explanation at all of WHY.
Actually a lot of Math teachers I met explain things in this way, which can be rather frustrating
What do you expect from an Asian?
I would say that's not her fault but more the fault of mathematics. There is no rule or formula to ever tell you what to do next. In mathematics the only good answer to why did you do this is "because it works"
Sometimes I ask my self what is the benefit of such math, it is like guessing not a direct math , useless in normal job life , don’t expect nowadays mobile / comp. generation children need such bla bla
@@somgesomgedus9313 Actually I must respectfully disagree. To suggest that "because it works" is the only explanation needed in maths encourages rote learning, instead of gaining a true understanding of what you are doing, and why. Mathematics is a language used for the manipulation of symbols: "because it works" is like learning the words of a spoken language without learning their meaning. It renders you helpless when faced with a novel situation, and that is not how we should teach maths.
Nicely done and thank you.
However, I'll just use my handy electronic calculator for these kind of problems.
When I went to a secondary modern senior school in 1958 I was taught to be literate and numerate, I worked as a precision engineer but I don't have a clue what the lady is talking about.
Bro this for real made me fall of my bed laughin
She got this "trick" out of a Deus Ex Machina
Kinda useless for ANY practical purposes ...sqrt(sqrt(9) -sqrt(8)) is solved using a pocket calculator
Not an Olympiad. It’s clickbait. No date given. Disliked and blocked
Being an IIT - JEE aspirant from India , It is one of the easiest category of maths problem I ever met !
I know the trick too.... But if anybody don't know the trick of solving it directly....they too have to give a minute..... Professor of college who are doing PhD in mathematics don't know such trick and they may take a minute to solve it's doesn't mean that they know less math than you okay...... I hope you otherstand the difference
@@mathematicsman7454 I am not judging anyone as If someone is able to solve this problem she may be genius and the one who isn't is weak in maths . I was just saying that even in Maths Olympiad , there comes questions which can be solved just by basics ! Well I respect your opinion ..
Thankyou for being my competition
And in IIT JEE we never got such questions
@@deepamurthy198 Yah !
Appreciate that there are some Maths Olympiad questions within our grasp.
I forgot the sqrt(square) trick from high school, but would have been able to do it then.
These are like IIT JEE questions, maybe training questions, those students would argue.
I expect IIT JEE students (even students) to call this easy by IIT JEE standard.
Which would make me average in Maths. At 90 percentile in Quantitative Ability in the Stamford-Binet V test.
yeah, it's an easy question. Like JEE Mains level probably.
@@eddie31415 this is class 9 school level.
This question is in Class 9 R D Sharma Factorisation of Polynomials fill in the blanks in the form of √3 -2√2.
@@eddie31415 lol no 8th or 9th class problem maybe jee mains level are far more harder than thiss
@@eddie31415 it's a grade 9th or 10th question maybe
it's for secondary school in Vietnam 😂
True story 😂
Because in the main question the number under square root is definitely positive, as squared root of 9 is bigger than squared root of 8.
Then again, the square root of 9 is also -3, so there are two answers.
@@scottrichmond3548 square root of 9 is 3 not -3
@@rudraroopbhattacharjee6191 what's -3 * -3 ?
@@antronx7 9
@@antronx7 I understand what you are trying to say but its a rule of mathematics that in Real numbers, √x is always non negative.
What you mean to say is-
Roots of X² are ±√(x²)
See, the ± comes before a square root thing. This is because a square root can never be negative.
In your case,
X² = 9
X = ±√9
X = +3, -3
I knew this ...i just forget about it. That's what happens when you don't stay in practice
Ashole cleaning in Hospital useless.
I am totally lost from the start.
√(3 - 2√2). Shortcut: 2 + 1 = 3 and 2 x 1 = 2. Automatic: √2 - √1 which simplifies to √2 - 1. Use the shortcut and don't overthink it.
i didn't get your point
@@killanxv If (1) the coefficient in front of the second term is 2, and (2) the numbers summing to the first term are the same as factors multiplying to the radicand in the second term, then the answer is the sum or difference of the roots of the two numbers summing to the first term. See my post above. Gotta have that coefficient of 2 in front of the radical sign in the second term. √(15 + √200)) √200 = √(4 x 50) = 2√50. Bingo! Got the coefficient of 2. Now 10 + 5 = 15 and 10 x 5 = 50. Throw radical signs over 10 and 5 for your answer: √10 + √5. Note that we keep the sign in the original problem. Hope this helps.
@@jim2376made even more difficult 😂 , what is a radicand ? Too simple earlier , it happens by simple instincts
@@abhishekchhikara4100That's for people like you, just go and read definitions and you can see the word radicand is so common in most textbooks
What happens when your teacher wants to see the problem worked step by step?
To simple 🙃
√( √9 - √8)
√( 3 - √8)
√( 3 - 2×1.41)
√( 3 - 2.82)
√( .18 ) => near to √16
So as my own formula 😂 ( work only when number are near to root )
Information √.16=> .4
√.18
.4 + 1/18
=> .4 + .056
=> .456 (it is approx without so much calculations 😅)
Well the 1/18 , its come from my formula
Like if someone root value are near to square
√24 = √25 - (25-24)/( *2* * 25)
*2* is constant 😊
I hope one day everyone finds the peace in math! Love from Türkiye.
Well we are not going to find it until we get fair question remember differential problem in 2021? İ dont know if youre university preparing student or you did but just check it out
I like maths...but I absolutely hate when they get "creative" (i.e.: the only way to resolve a problem, instead of using a well stablished and proven algorithm, is having a happy idea). Thank God for calculus.
What kind of pen are you using? I’ve been looking for a fine-point pen for ages!
I'm glad someone else asked this question.
3-2✓2 = 3-2*1.414 just product and subtract will give your answer
If this is a math-olympiad question, I'm a genius
do you all Know that math olympics have some simple questions here and there to slow participants down and reward faster solutions right?
This Its ONE example of such questions. You solve it quickly to have more time to solve the actual problems
Good luck with the other questions "genius"
This shows a technique, it is kept simple to make the point come across more easily. In a real question, this could be one step in the middle.
you're right: its not a math olympiad question. Clickbait
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
Olympiad?😂😂
Used calculator, got same result.💪
Work smarter not harder 💪
Great if u lived 100 years ago. Use ur damn phone 😂
I could have gone my whole life without knowing that answer! Now I know!
Please help me to solve using diff of 2 sq as mentioned by teacher but not followed.
We have Ramanujan Technique to solve this in the mind itself.
Why do you need ( a-b)(a-b)? You can simply find the answer at 3-2√2 only na. 3-2*1.414=3-2.828=.172=√.172=.414 which is the same one.
Im guessing you're not allowed a calculator in this exam , as such your calculation are only approximation and can't be used as answers.
@@lesouni9342 you don't need a calculator for such easy things.you don't even need a pen& paper for sure.
2+8= 10
Hiding qusoin are
Even though she is flexing she got the answer wrong it should be 0 .414
Bu soruları Türkiye'de ilkokul çocuğu çözüyor.
Primary school children solve these questions in Turkey.
Interesante y didáctica explicación, muchas gracias por compartir 😊❤😊
Calculator 🗿
What's the motivation for trying to express it as a^2 - 2ab + b^2? If you don't already know the answer, why would you do that?
This method is called compleating the square. You map your current problem on the binomial formula and then use it to simplify the problem. Which she did.
I did not watch the video with sound on. Not sure why everyone is so negative in the comments...
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
It would be easier if she did it according to Dekart's rule.
Now √(√9 - √8) = √(3 - 2√2).
Now suppose √(√3 - 2√2) = a + b√2, where a and b are integers. This maybe not actually have a solution in integers, but if it does, we can find them as follows.
Let 3 - 2√2 = (a + b√2)²
= (a² + 2b²) + 2ab√2
So, 3 = a² + 2b² and -2 = 2ab
So, (a = 1 and b = -1) or (a = -1 and b = 1).
However, a + b√2 ≥ 0, as otherwise √(√9 - √8) would be a complex number, so we are forced to conclude that a = -1 and b = 1 is the only possible solution.
So, √(√9 - √8) = -1 + 1*√2 = √2 - 1.
It can be the other method which is great but the standard one is more easy and convinnient
I'd start by relaxing to let a, b be rational numbers. Then be pleasantly surprised when they turn out to be integers. The rest of the process is exactly the same.
olimpiyat sorusu diye gösterdiği şeye bak mk 10.sınıf apotemi fasikülü daha zordu
Im very weak in math but somehow completed intermediate with 97% in math and completed my engineering a month ago 😂
No one asked
@@AdityaKumar-gv4dj No one answered you! Saala
A lot of work while there is simpler shot cut . Where did a and b come from
Why ? 😳🤷♂️
Bunları gördükçe kafayı yememek için kendimi zor tutuyorum
There is a rule if it is in the form of sqrt(sqrt(x+y)-2sqrt(x.y)) then the result is sqrt(x)-sqrt(y). For this question sqrt(sqrt(2+1)-2[sqrt(2)*sqrt(1)])=sqrt(2)-sqrt(1)=sqrt(2)-1
Well it's better to be said identity, since it holds for all Reals. Like a process has a rule to (for example) integrate by parts, you assume 1 function to be 1st and other to be second then you apply the formula of rule. Just my take.
This doesn't look exactly right. Square your RHS. You get (x + y) - 2 sqrt(xy). You need to lose one "sqrt" on the left hand side. To wit: sqrt((x + y) - 2 sqrt(xy)) = +/- (sqrt(x) - sqrt(y)), with the sign chosen on the RHS to ensure the number is positive.
37 years ago I had this one i my final high schools exam
I do not know how much time it would take for me until realizing that 3 - 2sqrt(2) can be easily presented in a form of a^2 - 2ab + b^2. Do mathematicians have a special ability to glance it on the spot when something can be recombined according to the known rule?
I think it is more about having experience and mastery with those tools. In many schools we skip to differentials and integrals before having a solid grasp on foundations of math. It's like they think mathematics was an intellectual desert up until newton and Leibniz. If students are educated to maximize their mathematical tools before learning new ones, they'd know how to solve these problems. (The Israeli school system is worse than the american, we don't even learn completing the square, so we'd have no intuition for solving this kind of problem)
@@TheMeiravital😂
@@TheMeiravital Thank God they did do that otherwise I would have failed math. Memorizing patterns is not as useful as understanding why. ESPECIALLY once you realize that in the real world math never works out nicely like that.
I thought I was the only one who had this shitty problem, I had to solve advanced math problems without having enough time to fully memorize algebra formulas due to lockdown. And now everyone is kicking ass
I think they just saw the same or very similar solutions over and over. I asked my math professor a question before and he solved it by adding 1 to the both sides of the equation. When I asked why would he do something weird like that and he told me that they just get used to this patterns over the years.
Why you use modulus?
As a Turkish student who studied for university entrance exam, I am really sad that I solved this question like in seconds from my mind.
So which University did you end up 😬 😁
@@SunriseLAWroasted
Funny how so many third world students come here to brag about being able to solve this.
@@egeozel80hes cleaning washrooms for a living
In1990ies in ist. muhendislik one of our friend proved a wellkown physics equation's incorrectnessby maths but these kids are smiling on you ,dont worry you're in the right path...
wrong Answer, more precisely incomplete answer
True solution=-(root(2)+1),(root(2)+1),(root(2)-1),-(root(2)-1)
Para los que piden solución negativa, recuerden que:
x^2=4
no es lo mismo que
x=√4
....
Esatto. Dai che a novembre quando non sarò più quello dei numeri e tiferò Putin che farà un bel botto nucleare vi regalerò giubbotti di plastica a specchio, piscine in muratura e motomacchine che sfrecciano a 500 orari. Da novembre ci divertiamo tutti contro tutti col finale nucleare planetario
pero cuadrados negatvos no existen
2+2 =4
4+4 = 8
هدا. احتيال. بالرياضيات. الحل. نجد قيمه. طرح جذر ٢ من. ٣
وتكون. الاجابه. ١،٦ تحت. الجذر. ليكون. الجواب. هو. ٠،٤. وهذا. نفس. جوابكم.
Funny i always thought algebra was magical until i learned trigonometry. Then i was amazed on how it is used in daily life. I always questioned when i would need to use algebra in daily tasks... 😅
Why did the math book look sad?
Because it had too many problems!
Please do not write sqrt(2)= 1,414 This was the moment when you lost me.
@@buddy0479 You are mistaken. In the UK it is also 1.414. It is other European countries such as France and Germany where this occurs.
To solve the given expression, we can simplify it step by step:
Simplify the square root of 9: v9=3
Simplify the square root of 8: v8=2v2
Substitute the simplified values back into the original expression: v3-2v2
Therefore, the solution to the given expression is v3-2v2
It would be interesting to see this used in an actually useful use case. My brain has a hard time following nonsensical “just because” problems
What do you define as an actual "useful use case"?
Find the roots of x^4-6x^2+1
@@lestath2345 tell me a real world instance where this would be used other than a math class
@@WoodrowWoods2007 In the field of pure math. Also, we're mostly doing this for the sake of doing it, just like playing video games, *for fun*.
@@lestath2345yes it is a brain exercise. Opens the horizons of brain
I never used the (a±b)² formula like that before, thats brilliant
2+2= 4
As an Indian, I appeared this question at SOF Mathematics Olympaid in my third grade
I always see Indians in comment section only to brag about themselves. Usually this means a lack of confidence and self-respect. Is India one of the leaders in technology in the world?
I can not believe this is Math Olympiad question. Dumbing down populus.
I got the answer as soon as i saw it 😂 i remember 40 years ago my teacher still be asking for the pointless work lol
The answer is 1 -one- 😉👌🏼
I don't like abstract short cuts. Too complicated.
Türkiyede bunu yapamayan okul okuyamaz 😂😂😂
As Indian I can confirm this we did in grade 6
Куда ещё один (отрицательный) корень сπздили?
I love maths but the way she explains it its juicy way of explaining.
Use a calculator!
It is faster!
√{a ± b√c} (a,b,c non-neg. rat.) can be simplified to √y±√z iff {a² - b².c} = d².
If this d exists, then take y = (a+d)/2 & z = (a-d)/2. Here a=3, b=2, & c=2.
So d = √{3² - 2².2} = √{9 - 8} = √1 = 1. So y = {3+1}/2 = 2 & z = {3-1}/2 = 1.
Hence √{√9 - √8} = √{3 - 2√2} = √y - √z = √2 - √1 = (√2) - 1.
What does the last instruction read. Is it English? I couldn't decipher.
2+2=4
3_2 1
2_ 0
2_ 1 0
*Indian students are solving such peoblems in 9th and 10th standards 😂😂😂😂*
*And you guys are solving it in Olympiad level 🤣🤣🤣🤣🤣*
To solve the problem here, two symbols used ie. "Is equal to" and "implies". For simplification "is equal to" is used. But to solve an equation "implies" symble is used.
Can you specify the implies symbol?
This can’t be olympiad question. It is literally one of the math 101 rules. There is even shortcut for that like people mentioned.
do you Know that math olympics have some simple questions here and there to slow participants down and reward faster solutions right?
This Its one example of such questions. You solve it quickly to have more time to solve the actual problems
@@eliasbram3710 heh
We were solving such problems in my 9th grade in Romania in a regular maths class. Too simple for an Olympiad.
Please help me to solve this using the diff of 2 sq as the teacher mentioned but she did not use this instead she said 2+1.
Bruh why u calling it olympiad level? Its very easy for a 8th grade student....
In Asia, a bad student in 2nd school can easily do this math :))
I'm sorry, but your use of "=>" is amateurish and wrong.
Why does the final answer have to be positive?
the root of x square = module x(module≥0)
@@flam1ex186 a square root can be both positive and negative
@@sureshmukhi2316 that is true for complex numbers/functions. For reals it must be positive.
Root doesn't contain negative
If a root can't be negative then explain the quadratic formula?
This is not a Math olympiad level question. It's an ordinary mid-school exam level at best.
Very interesting, although in practice it is not needed for anything in life :)
In everyday life no, but the general take away from problems like this is exercising the notion of manipulating mathematical expressions into different forms to make them simpler (i.e., easier to manage, interpret, etc).
This particular example isn't that complicated, but the general skill of simplification can come in handy in certain jobs. Like if one were to come up with a certain formula to describe a particular phenomena that's unique to that company, someone else may want to manipulate the form of that formula so to make its terms more explicit.
@@chrisjfox8715bruh
Certainly you won’t need it don’t worry
It's just for improving your thinking skills.
You don't, but the smart people do
Básicamente...not solve anything but reduce or create numbers
Очень легкая и известная задача
Средний вопрос олимпиады по математике в Юпитере
Ключевое слово "известная". Всё легко и просто, когда известно. Жаль, что до людей не доходит элементарная вещь
Very amateur solution. This women is not a professional mathematician! (1) Some notation issues: The logic IMPLICATION symbol cannot substitute the equality symbol!!! The dot at the bottom cannot be used in a confusing way: if we want to represent multiplication, the dot should appear little higher , in the middle of the height of small letters . It can not be used in the same way as the decimal point (2) WHY her method works? There is not any commentary regarding the resolvability of the problem. Her method to simplify nested square root expressions [sqrt ( sqrt (a) - sqrt(b) ) ] is only working iff a-b is a PERFECT square. First this statement should be proven. After what we can attack the problem. (3) The women is not aware of the difficulty of real maths competition problems, if she is considering this one as an olympiad challenge.....A computation is only a computation. Nothing else!
You’re clever and gorgeous ❤❤❤
This will not come in SG math olympiad. they be testing quadratic formula and equations for junior.
This is actually really simple for an olympiad 😂
I have a backlog in math, so not a qualified person to address this, but any question is hard if you don't know the method to solve it. You know this already, sweetheart...❤
I am a student
Can you tell me what I did wrong trying to solve this
√((√9)-(√8))= x
√9-√8=x²
9-2×√9×√8+8=x⁴
9-2×3×2√2+8=x⁴
17-12√2=x⁴
x=fourth root of 17-12√2
But the answer I'm getting is 0.4142135.....
Which is also the same answer I'm getting for √(√9-√8). (0.4142135.....)
Edit: I'm an idiot I thought you said the answer is sqrt of 2, didn't hear the part where you said sqrt of 2 -1, that makes a lot more sense. So my answer is correct.
Clickbait video. It shows your inexperience when you use => rather than =. Stop calling every silly math question a *olympiad* one. At least mention which *olympiad* it is.
I tried 2sqrt3b + b^2 = -2sqrt2, solve for b. Damn I got sqrt 3 + b, where b = -sqrt3 + sqrt(3-2sqrt2) = the original equation 😂
If this is maths Olympiad level question then I am Srinivas Ramanujan , c’mon I am in class 9 and solved it mentally (2027 jee aspirant)
Math olympiad question? Hahahaha
We tell this to our 9th graders. I've rarely seen anything more ridiculous.
Instead of doing this simply let the whole thing be x and form a quadritic equation and just solve it. Isn't it better to give all the possible values rather than just 1 value?
This is a standard problem. You reduce it to sqrt (sqrt (9)+sqrt(8))=sqrt (2+2\sqrt(2)+1)=sqrt(2)+1.
C’est compliqué tu es trop expliqué donc racine carré 9=81 et racine carré 8=64 ; racine carré 9-racine carré 8 = 17
Come on guys it is for 5th or 6th olimpiad problem ❤ Don't criticise this is too EASY
In Bangladesh, these types of problems are taught in Seventh Standard
This is not a trick, come on, there is a principle behind it, no doubt, but you missed explaining it. It's a plai Deux Ex Machina going from the radical to the general formula of a 2nd degree polynom