or horner scheme also i ve never seen an english speaking channel using the pq formula to solve quadratic problems, almost no one that i ve personally met used abc formula lol
Getting x = -3 is easy enough Though instead of factoring the function to solve for the rest of the x values, I used synthetic division on the equation x^3 - x^2 + 36. Then I used the quadratic formula like you did and got the last 2 answers.
I just used common sense that x³ will grow faster that x² graph so it had to be a negative number, and -3 was the only number which could bring the answer. Secondly if we take the x² term to 36 side and plot the graphs for x³ and x²-36. These will intersect only once in real axes, which is x=-3.
In this case i like to use the minimal form of the quadratic formula because b is a multiple of 2 so we'll have: x = - b/2 +o- √(b/2)^2 - ac all over a
There are three solutions. Obvious x=-3 and two others. Just divide Polynomial /(x+3) Horner's method is the fastest. Then use quadratic roots formula.
@@Edek_Zgredek800 yes but that does not make the answer -3 Incorrect, or some what right. It IS a correct answer and it satisfies the equation. Sure there are more ways to do it, but that does not make this answer less correct.
my method: given that x squared has to be less then x cubed because x^2-x^3 > 0 we know that x has to be negative. we also know that x has a lower bound of more than negative six because any more would cause the paradox x^2 >= 36 and x^2+x^3=36 and by transitive property that would become x^2=x^2+x^3 which just becomes x^3=0 which cannot be true cause 0^2-0^3 != 36. we also know that x has to be an integer because any two non integer numbers greater than 1 multiplied also do not result in a whole number. we can also find out that the lower bound is actually 4 because any more would cause for us to add 4^3 to a positive number which would result in a number greater than 36. now we know it is either -1, -2, or -3. -1 can be ruled out because it would all just become 1+1=2, and now we can just plug in -2 which fails, and -3 which is the answer.
1:51 You forgot to explain how you came up with this way of rewriting the equation. You could have said that x=-3 implies that one factor is x+3 so we need x³ combined with +3x² so that we can rewrite it as x²(x+3).
Learnt from habit (don't be hasty) that not every video is click bait. I got -3 instantly after seeing the problem, but just had a hunch that there's more to it since it's a cubic expression.
I just used basic factors x^2-x^3=36 Since the answer is positive x squared is bigger than x cubed And x=negative number And then take factors of 36 2,3,4,6,9,12,18 And try taking each as a negative number Luckily the number stopped on 3 so -3^2- -3^3=36 -3^2+3^3=36 9+27 =36
So, I got -3 as my answer from the thumbnail. Subtracting what should be a larger number from a smaller, and getting a positive integer made me suspect a negative was involved. So, I then figured, 'what squared added to itself cubed is equal to 36?' 2 was out, because that would only be 4 and 8, making 12. 3, however, gave 9 and 27. add 27, or subtract -27, and 9, and you get 36.
Welp, I just knew that x would be a negative number seeing that you get a positive number by subtracting a smaller number, therefore I calculated by making x -4 first and then -3 and boom! The answer is x = -3
After thinking for a while and realizing x had to be negative, I came up with -3. But I don't know how to derive that solution. I used educated guess and check.
First, I saw that x had to be negative, otherwise it would be impossible, next, I saw that x would have to be at lest 6 or less cause 6^2 is 36, now you have that x could be equal to -(1-6). After trial and error, -3 is x.
That's the base school question,so you're lying in the start of the video, saying that it is "most difficult math olimpiad qestion" that not even olympiad
Square-cube= (+) ve ; so the value of x must be in negative Cubic numbers less than 36 are 8,27 36-8=28, must be wrong 36-27=9=(-3)² The answer is -3🤷 (Idk I can't solve things normally using typical formulas)
it took me 1-2 mins but anyone can solve this by just proving its -3 by inputing the value . Still though it was quite easy I got it from the thumbnail
Ngl I just solved it with trial and error. I saw it was x×x-x×x×x so I knew it had to be a negative number then I just started with the number -2 and went up so first I did -2×-2--2×-2×-2 which is 4--8 which is 4+8 which is 12 so I scrapped that and went to -3 so I did -3×-3--3×-3×-3 which is 9--27 which is 9+27 which is 36
We know that X is negative from the beginning, we know that 1 - X equals 36 over x²... so 1 - X equals 1 or 4 because neither 6 or 12 have integer roots and -8² is bigger than 36. If you have a good memory X is not equal to 0 so 1 - X needs to be four, Wich makes X equal to minus 3
(Haven’t watched the video yet) I first thought that x should be negative because a negative value of x would make x^2 a positive, and -x^3 a positive. And a positive added up to a positive will equal a positive. Then, I pretty much guessed -3 as a nice number to start guessing and checking, and got it right. As you said, it’s basic logic.
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If Harvard entrance questions are this easy something’s up. I solved the question from the thumbnail bruh.
Wow so you got 2 + or - 2 root 2 i?
It really is
@@SillyPerrin yeah that was the hard part
Same to me bro
Me also lol, it's our school grade questions
Just use cubic formu…
😡😠
**gets shot**
Factoring is easier than trying to remember that
Cubic formula needs to have an X term as well broda
@annanay007 c = 0
x=-3 is easy to see. Then you have to do the polynomial division x^3 - x^2 +36 : (x+3) ,which leads to a qudratic equation.
or horner scheme
also i ve never seen an english speaking channel using the pq formula to solve quadratic problems, almost no one that i ve personally met used abc formula lol
Getting x = -3 is easy enough
Though instead of factoring the function to solve for the rest of the x values, I used synthetic division on the equation x^3 - x^2 + 36.
Then I used the quadratic formula like you did and got the last 2 answers.
I just used common sense that x³ will grow faster that x² graph so it had to be a negative number, and -3 was the only number which could bring the answer.
Secondly if we take the x² term to 36 side and plot the graphs for x³ and x²-36. These will intersect only once in real axes, which is x=-3.
In this case i like to use the minimal form of the quadratic formula because b is a multiple of 2 so we'll have:
x = - b/2 +o- √(b/2)^2 - ac all over a
-3
Solved in my brain in less than 30 seconds
33% correct!
@@brain_station_videos 33.33333333..........% correct
@@brain_station_videos how is it 33% right? If you plug in -3 as x you get 36, so -3 satisfies the equation, what's the issue?
There are three solutions. Obvious x=-3 and two others. Just divide Polynomial /(x+3) Horner's method is the fastest. Then use quadratic roots formula.
@@Edek_Zgredek800 yes but that does not make the answer -3 Incorrect, or some what right. It IS a correct answer and it satisfies the equation. Sure there are more ways to do it, but that does not make this answer less correct.
So there's this thing called synthetic division
I did this mental math! easy! -3 is the real answer!
I too
my method:
given that x squared has to be less then x cubed because x^2-x^3 > 0 we know that x has to be negative. we also know that x has a lower bound of more than negative six because any more would cause the paradox x^2 >= 36 and x^2+x^3=36 and by transitive property that would become x^2=x^2+x^3 which just becomes x^3=0 which cannot be true cause 0^2-0^3 != 36. we also know that x has to be an integer because any two non integer numbers greater than 1 multiplied also do not result in a whole number. we can also find out that the lower bound is actually 4 because any more would cause for us to add 4^3 to a positive number which would result in a number greater than 36. now we know it is either -1, -2, or -3. -1 can be ruled out because it would all just become 1+1=2, and now we can just plug in -2 which fails, and -3 which is the answer.
Solved in under a minute. Easy for me, but if you don't understand numbers...
1:51 You forgot to explain how you came up with this way of rewriting the equation. You could have said that x=-3 implies that one factor is x+3 so we need x³ combined with +3x² so that we can rewrite it as x²(x+3).
X=-3 x²=-3×-3=9 and x³=-3×-3×-3=-27
The equation is x²-x³=9-(-27)=9+27=36
Learnt from habit (don't be hasty) that not every video is click bait.
I got -3 instantly after seeing the problem, but just had a hunch that there's more to it since it's a cubic expression.
Naa i brutefoce it:
x² - x³ = 36
x²(1 - x) = 36
i) x² -> fac(36)
II) 1-x -> fac(36)
fac(36) = {
1, 36
2, 18
3, 12
4, 9
}
pfcSqr(fac(36)) = {
1, 4, 9
}
Case x²=1, (1-x) = 36 => x = ±1, x = -35
Case x²=4, (1-x) = 9 => x = ±2, x = -7
Case x²=9, (1-x) = 4 => x = ±3, x = -3
Therefore: x = -3
Yes but that's only one of the solutions, We need to find all the solutions
@@tuwrgames well after dividing it the eq become quadratic and I know man u can do it
x=−3,x=
2
3+i
39
,x=
2
3−i
39
I just used basic factors
x^2-x^3=36
Since the answer is positive
x squared is bigger than x cubed
And x=negative number
And then take factors of 36
2,3,4,6,9,12,18
And try taking each as a negative number
Luckily the number stopped on 3 so
-3^2- -3^3=36
-3^2+3^3=36
9+27 =36
1:40 honesty when you know that x should be -3 you could just use the Horner's method to skip instantly to the quadratic equation
x = - 3, 2+ 2√2 & 2 - 2√2
Nope
@brain_station_videos read 2+2√2i
& 2 - 2 √2 i
Kas app mera math ka teacher hota pura school math topper hota I am your big fan i am really love your videos
Damn how is bro understanding hindi
@@annanay007 google translate😂
@@annanay007He isn't.
@@Gaurav_Yadav_7Google translate doesn't work for that type.
The thumbnail ain't the same as the problem
So, I got -3 as my answer from the thumbnail.
Subtracting what should be a larger number from a smaller, and getting a positive integer made me suspect a negative was involved.
So, I then figured, 'what squared added to itself cubed is equal to 36?'
2 was out, because that would only be 4 and 8, making 12.
3, however, gave 9 and 27. add 27, or subtract -27, and 9, and you get 36.
Minus three, by inspection.
*x² - x³ = 36*
*x² - 9 - x³ - 27 = 0*
*(x² - 3²) - (x³ + 3³) = 0*
*(x + 3)•(x - 3) - (x + 3)•(x² - 3x + 9) = 0*
*(x + 3)•[x - 3 - (x² - 3x + 9)] = 0, so either*
*x + 3 = 0 -> x = -3, or*
*x - 3 - (x² - 3x + 9) = 0*
*x² - 3x + 9 = x - 3*
*x² - 4x + 12 = 0*
*From there, the two complex solutions are x = 2 ± 2i√2. So where is my Harvard diploma?*
Algebra 2 is not harvards hardest questioned
My dumb as brain thought it's ( 3i^2 ) seeing the thumbnail 😂😂.
not me trying it and getting x is undefined 💀
💀✌️
-3, solved in my head with only the thumbnail
I got -3 immediately off the top of my head. Never saw this problem before, it was just easy
Partially correct
Welp, I just knew that x would be a negative number seeing that you get a positive number by subtracting a smaller number, therefore I calculated by making x -4 first and then -3 and boom! The answer is x = -3
33% correct!
x^2•(1-x)=36
(-3)^2•(1+3)=36
(x^3-x^2+36)/(x+3)=x^2-4x+12
x=-3 or x=2+-2isqrt(2)
Why do this long method, you can pretty easily see that it’s just -3
After thinking for a while and realizing x had to be negative, I came up with -3. But I don't know how to derive that solution. I used educated guess and check.
First, I saw that x had to be negative, otherwise it would be impossible, next, I saw that x would have to be at lest 6 or less cause 6^2 is 36, now you have that x could be equal to -(1-6). After trial and error, -3 is x.
as a middle schooler it makes but not really
6^6 2^3^2^3 1^1^2^3 2^3 (x ➖ 3x+2).
That was very easy. I just looked at it once and thought -3 and it worked out lol.
So you guessed?
@ Nah guess is not really the right word.
There is no Harvard entrance exam...
did that in 11th grade in highschool.... Harvard isn't what it used to be....
2:42 bro here's a mistake it is -12 you have written 12
No its 12 only. Pls check again
@brain_station_videos no bro you take (x-3) which means (x+3) left and it has to be multiplied by -4 => -4x-12
-3 and then Horner system 😊
This is one of the JEE advanced type questions
Tell me you don't study without telling me you don't study
If this was the level of JEE advanced questions then the selection ratio would not have been only
This type of questions are not even asked in 10th board 3-4 marks section 😂😂
@@gamingroomdbxvdbzwithomjay1622 bro is preparing for Jabardasti Entrance Exam
😂😂😂😂
That's the base school question,so you're lying in the start of the video, saying that it is "most difficult math olimpiad qestion" that not even olympiad
It may be an easy question for you, but many people find this question difficult.
It is given to our math exam.so,why you write thumbnail that is an olympiad exam
How's this difficult? X2 - x3 can only be positive if x is negative. Hence x can only be 3
x^2(1-x) =36
9x4=36
x^2=9 and 1-x=4
So x=-3
Me, an 8th grade student: This is 10² - 4³ = 36.
Dude it's x² - x³ = 36 and not x² - y³ = 36
I can understand. You're still in 8th grade
Bro why are u yapping on this much easy ques 😭
I thought that:
x square - x cube = 36
-36 = x cube - x square
x = -36
Silly me😂😂
Lol 😂
x² - x³ = 36
Let us take x as -3
(-3)² -(-3)³
9 -(-27)
9 + 27 = 36
I forgor that this is Trial and error method
Square-cube= (+) ve ; so the value of x must be in negative
Cubic numbers less than 36 are 8,27
36-8=28, must be wrong
36-27=9=(-3)²
The answer is -3🤷
(Idk I can't solve things normally using typical formulas)
i solved it in my head -3
Partially correct
x²(1-x)=36
1-x=36
x1=-35
x²=36
x2,3=±6
That only works for when it's equal to 0 such as x^2(x-1)=0
it took me 1-2 mins but anyone can solve this by just proving its -3 by inputing the value . Still though it was quite easy I got it from the thumbnail
Its either ±6 or -35
I got -3 in my head 💀
X=-3
Ngl I just solved it with trial and error. I saw it was x×x-x×x×x so I knew it had to be a negative number then I just started with the number -2 and went up so first I did -2×-2--2×-2×-2 which is 4--8 which is 4+8 which is 12 so I scrapped that and went to -3 so I did -3×-3--3×-3×-3 which is 9--27 which is 9+27 which is 36
Bro just literally called -3 minus 3 😂
That's how you say it....
Negative and minus are the same....
Do you know how math works?
@@cosmiccoder0i think he is more used to saying negative three and thus pointed out a "mistake"
@@mekaindo alright, it's just i realised that I interpret math more differently than others, so I got angy 😡
x is -3, I literally bruteforced it in the first 10 seconds, am I goated like everyone in the comments?
How exciting🤭.
-3, easy, next.
-3?
-3 👈 Major
It was so easy though, x = -3
Bro just visualise it and u get x = -3
Is it really that hard?
I solved it in 20 sec
We know that X is negative from the beginning, we know that 1 - X equals 36 over x²... so 1 - X equals 1 or 4 because neither 6 or 12 have integer roots and -8² is bigger than 36. If you have a good memory X is not equal to 0 so 1 - X needs to be four, Wich makes X equal to minus 3
It's basically just logic
(Haven’t watched the video yet) I first thought that x should be negative because a negative value of x would make x^2 a positive, and -x^3 a positive. And a positive added up to a positive will equal a positive. Then, I pretty much guessed -3 as a nice number to start guessing and checking, and got it right. As you said, it’s basic logic.
muito bem bruno é assim mesmo
@@BRUNOHENRIQUE-fk6jtBrother you only got 1 answer, it’s a cubic
I was so wrong.. i had it as 42
Synthetic division?
I did polynomial theorem instead
x²-x³=36
x²-x³-36
x²-9-x³-27=0
(x+-3)-(x+3)(x²-3x+9)=0
(x+3)(x-3-x²+3x-9)=0
x=-3; x²-4x+12=(x-2)²-8(i)²=(x-2+-2√2i)=0
x=-3; x=2+2√2i; x=2-2√2i
im so confused
i think its fine anyway, im in ks3
I COULD SOLVE IT REALLY
Pls tell me why the fourth step is a^2-b^2 but not a^2+b^2
Only me the I fell the video seems made by AI
xx has 7 xxx has 29 this is not for youtube
Can t you just use horner's method
Yeah I was thinking exactly that
e: while watching this 11:00
Sooo good
Woahhh
This problem isn't interesting not is it Olympiad level. I could solve this problem when I was 13 years old in about 3 minutes.
Cap unless you live in Any Asian county or maybe UK
I think you need to learn more
-3
A video made by AI, narrated by AI. So bad.
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-3
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