Lol me too, i guess we Indians are taught to go through problems fast. When I saw quad equation going in higher degrees, i went back to the problem again and solved it instantly using Pythagorean triplets. 😂
I did the same thing. By 3:40 the process devolved into a glorified guess-and-check anyway on the assumption that the solution was a rational number, which is no different than what we did. He might as well have applied that reasoning much earlier in the process and done this far faster, and without needing the rational root theorem. He technically assumed it was merely rational, not a whole number, but it was an assumption nonetheless and much more work.
it's really nice to see how you solve it differently than I was taught in Brazil (where I live). for example, we don't "subtract/divide both sides", we essentially do the same things but we say we are swapping the term side (and changing the operation, so obviously 2x = 8, and we bring the 2 that is multiplying to the right side, where it now divides, so x = 8/2 = 4). we also call the quadratic formula Bhaskara's formula for some reason. anyways nice video!!
The bhaskara thing is an mistake that someone made more than a hundred years ago that became popular, probably cause it’s way better to say bhaskara than “fórmula do polinômio de segundo grau”
It could be shortened if you find the C for the big triangle and substract with x and then put it into the c^2=a^2+b^2 formula and it wil be like this 100=(x-3)^2 + (( surd 2x^2+2x+25)-x) and you will get x=11
Aqua Green. I'm flabbergasted how this channel doesn't have a million+ subscribers. Andy you're such a smart and intelligent guy. Sorry if my english was bad, but you did a great job!
Red! Awesome video, any polynomial above a degree of two just makes me want to cry. As an aside, I was working on this problem that asked how many factors a certain number had (it was some highly composite number, I want to say 600?) My immediate thought was to get the prime factors and count from there, as you did in the video. But I was having some trouble with the combinations. Maybe I'm just a bit rusty and need to relearn my combinatorics, but do you have a suggestion on how to go about it?
First find the prime factors. 600 has a prime factorization of 2^3 * 3 * 5^2. Every factor will be a combination of these prime factors. Each prime factor has 1 plus its exponent as the number of ways you can add it into a factor (0 copies, 1 copies, 2 copies, etc.), so you can use the fundamental counting principal. In this case you would get (3+1)(1+1)(2+1)=4*2*3=24 factors. Hope this helped. I could provide some clarification if this was not clear.
Orange. Because of your videos I'm starting to realize that mathematics is about have more and more weapons (formulas) in your toolkit and being creative with where and how to apply them. A 3,000ft view that I never recognized when studying math in school. Thank you for this window into the next level of understanding mathematics.
I got the correct answer WAY faster, although I made an assumption. That the bottom left triangle was a scaled version of the 3, 4, 5 right angle triangle. (with all sides being double) Which was a good assumption if the problem was gonna have a nice solution. 😂 And fav color is blu
Oh my God, literally today I was working on a problem and realized I could use the Rational Zero Theorem but I didn't remember it, and couldn't find anything in writing that I could understand. However, seeing it actively performed in front of me really helps with that! I also didn't realize, but I guess I needed a refresher on polynomial long division! Oh and if you're curious, the math problem was: "A+B+C=1 A²+B²+C²=2 A³+B³+C³=3 What is (A,B,C)?" I'm only using algebra and so far that's been cruel, I'm seven pages into it and probably inefficiently solving it, but I'm doing it until I got the answer without a calculator for some reason!
At this type questions i first check if there is a special triangle. (3-4-5, 5-12-13, 8-15-17, 7-24-25) Difference of big triangle's edges is 7. so i tried 8 15 17 triangle and it fit perfectly.
For the first time I'm gonna pause lol. The triangle with hypotenuse 10cm means the sides are 8 and 6; 64 plus 36 is 100 which are the squares. Since the side that's 8 is x-3 then x=11 (8+3). Unless I'm missing something (which is what I'm guessing) or you're going for a longer route I don't see where it's long Ok I like the longer method but since the result is the same I'd say I prefer the shorter route lol
You should use a method this method worl like let the polynomial equal to any function called P(X)and just replace x with the numbers are you using for example Let a polynomial x^2+2x+1 We know that one of root is 1 We just check it out by just replacing x with the numbers negative 1 because one of the root is 1 then X+1=0 so,x=negative 1 that's the reason we replace x with -1 Just check it out now P(x)=x^2+2x+1 P(-1)=(-1)^2+2(-1)+1 =1+(-2)+1 =0 5:09
Purple! I hated math in school (back in the 50's and 60's - crappy teachers made math boring/confusing) -- but I love solving puzzles and I've always been good with all the sciences (except for the math part that I have just always avoided). Anyway - watching your videos makes math seem fun and maybe it's not too late for me to start learning math at 70 years old?
I have discovered your videos recently, and I noticed you always detail how you get from (a+b)² to a²+2ab+b². I don't know in your country, but in France we are taught what we call "identités remarquables" (remarkable identities) that we are supposed to know: (a+b)² = a²+2ab+b² (a-b)² = a²-2ab+b² (a+b)(a-b) = a²-b²
I just plugged in 11 to start with figuring we had a 3/4/5 (6/8/10) triangle. Doing so makes the large triangle an 8 15 17 triangle. 17-11 = 6 which confirms the 6/8/10.
Purple, this was really good. It would be cool to have a test that's like one massive question like this. except I realized there's a big issue if I'm wrong
After I saw the triangle with c=10 I just knew x was either 9or 11 since you need legs 8 and 6 to get a hypotenuse of 10, and plugging in those two x values into x gives you 8 or 6
mint! at that point where there are too many x inside the equation i would probably just look at the multiple option and try the answer one by one see which one is correct
Pretty sure you know from the beginning that x is 9 or 11 because the 10 hypotenus makes the first triangle a special right and the known side has to be 9 or 11. From there you take 9 and assume a is 8 or take 11 and assume a is 6. Then pothag the big triangle to check whether the hypotenuse equals x+6 or x+8
Red, though I first worked through all the ways to use quadrilateral formulas. The other missing side length is non integer and made a hash of things. Doing the quadrilateral area formula against the sum of triangles became a mess. Discarding that I did as you dud in a more convoluted way. Rather than struggling through finding the roots of the quartic, I threw it into a spreadsheet, plotted and quickly solved it that way. Though not proper for this sort of solution, 50 years of engineering on - I use them a lot to bash through problems. But then too, I tend to solve for all of the missing elements and nit just the one sought in the problem statement. Force of habit.
Orange! Ok I’m going to go buy a high school math textbook and brush up. It’s been too long since I’ve done this.
NO WAY YOU LIKE ORANGE TOO?!??!!??!?
Orange fucking rules 🔥🔥🔥🔥☝️
ruclips.net/video/q7M-TlRioPo/видео.htmlsi=qOYCl3JEzo6-NzcP
@@lucarroba WE BE MAKING OUT OF THE HOOD WITH ORANGEE 🗣 🗣 🗣 🗣🔥🔥🔥🔥
Santra
blue. i cheated a little by checking for the pythagorian triplet 6-8-10, and substituted for x accordingly. got x = 11 on my first try!
it's not cheating, its clever way of solving, i did the same 😂😂
Lol me too, i guess we Indians are taught to go through problems fast. When I saw quad equation going in higher degrees, i went back to the problem again and solved it instantly using Pythagorean triplets. 😂
I did the same thing. By 3:40 the process devolved into a glorified guess-and-check anyway on the assumption that the solution was a rational number, which is no different than what we did. He might as well have applied that reasoning much earlier in the process and done this far faster, and without needing the rational root theorem. He technically assumed it was merely rational, not a whole number, but it was an assumption nonetheless and much more work.
the question would be 10 times faster if the question stated “x is a positive integer” 😂
nah, length of side cannot be negative by default there is no need to state that
@@shivtheunknown I mean there is abstract geometry
@@shivtheunknown It's not about the positive but the integer part. There would be only 11 different possibilities if it said that
nope, if x is a integer than you can immediately tell from the (x-3),y,10 triangle that it is a 8,6,10 triangle hence x=8+3=11@@misteroking
Blue-green. I haven't needed to do math problems in years, but I still love your videos. I even vaguely remember some of the things you talk about. 😆
it's really nice to see how you solve it differently than I was taught in Brazil (where I live). for example, we don't "subtract/divide both sides", we essentially do the same things but we say we are swapping the term side (and changing the operation, so obviously 2x = 8, and we bring the 2 that is multiplying to the right side, where it now divides, so x = 8/2 = 4). we also call the quadratic formula Bhaskara's formula for some reason. anyways nice video!!
Where i'm from the quadratic formula is called "the second degree polynomial's solving equation".
@@jamasa007 omg that's so long 💀
@@blueberrypie3141 its only 4 words in my language
It is called 'Dharacharya vidhi' here
The bhaskara thing is an mistake that someone made more than a hundred years ago that became popular, probably cause it’s way better to say bhaskara than “fórmula do polinômio de segundo grau”
Puce. Because no one ever says puce is their favorite color. It's too purple to be pink and too pink to be purple. How exciting.
The colour of your eyes 😳
It could be shortened if you find the C for the big triangle and substract with x and then put it into the c^2=a^2+b^2 formula and it wil be like this 100=(x-3)^2 + (( surd 2x^2+2x+25)-x) and you will get x=11
Exactly what I did
Blue/green. Your videos are helping me brush up on the basics in preparation for having to help my kids with their math homework
Aqua Green. I'm flabbergasted how this channel doesn't have a million+ subscribers. Andy you're such a smart and intelligent guy. Sorry if my english was bad, but you did a great job!
Blue man 7:00 love your videos keep posting more of them pleass
Red! Awesome video, any polynomial above a degree of two just makes me want to cry.
As an aside, I was working on this problem that asked how many factors a certain number had (it was some highly composite number, I want to say 600?) My immediate thought was to get the prime factors and count from there, as you did in the video. But I was having some trouble with the combinations. Maybe I'm just a bit rusty and need to relearn my combinatorics, but do you have a suggestion on how to go about it?
First find the prime factors. 600 has a prime factorization of 2^3 * 3 * 5^2. Every factor will be a combination of these prime factors. Each prime factor has 1 plus its exponent as the number of ways you can add it into a factor (0 copies, 1 copies, 2 copies, etc.), so you can use the fundamental counting principal. In this case you would get (3+1)(1+1)(2+1)=4*2*3=24 factors. Hope this helped. I could provide some clarification if this was not clear.
Orange. Because of your videos I'm starting to realize that mathematics is about have more and more weapons (formulas) in your toolkit and being creative with where and how to apply them.
A 3,000ft view that I never recognized when studying math in school.
Thank you for this window into the next level of understanding mathematics.
Red brother
REally enjoy watching your videos and made me like solving maths related problems a lot.
I got the correct answer WAY faster, although I made an assumption. That the bottom left triangle was a scaled version of the 3, 4, 5 right angle triangle. (with all sides being double) Which was a good assumption if the problem was gonna have a nice solution. 😂
And fav color is blu
Blue-ish grey, what a splendid mathematical approach to this problem!
Oh my God, literally today I was working on a problem and realized I could use the Rational Zero Theorem but I didn't remember it, and couldn't find anything in writing that I could understand. However, seeing it actively performed in front of me really helps with that!
I also didn't realize, but I guess I needed a refresher on polynomial long division!
Oh and if you're curious, the math problem was:
"A+B+C=1
A²+B²+C²=2
A³+B³+C³=3
What is (A,B,C)?"
I'm only using algebra and so far that's been cruel, I'm seven pages into it and probably inefficiently solving it, but I'm doing it until I got the answer without a calculator for some reason!
Blue/green! Great walk through defintely do more of these
At this type questions i first check if there is a special triangle. (3-4-5, 5-12-13, 8-15-17, 7-24-25) Difference of big triangle's edges is 7. so i tried 8 15 17 triangle and it fit perfectly.
Green. These are really enjoyable! I'm thrilled I found your channel
For the first time I'm gonna pause lol. The triangle with hypotenuse 10cm means the sides are 8 and 6; 64 plus 36 is 100 which are the squares. Since the side that's 8 is x-3 then x=11 (8+3). Unless I'm missing something (which is what I'm guessing) or you're going for a longer route I don't see where it's long
Ok I like the longer method but since the result is the same I'd say I prefer the shorter route lol
What if the side you think is 8 is in fact 6? You will have to test for that?
All of them! Thanks for your work!
this is more fun than sport
Dark blue, I don't think I am sane enough to do this but I am stupid enough.
You should use a method this method worl like let the polynomial equal to any function called
P(X)and just replace x with the
numbers are you using for example
Let a polynomial x^2+2x+1
We know that one of root is 1
We just check it out by just replacing x with the numbers negative 1
because one of the root is 1 then
X+1=0 so,x=negative 1 that's the
reason we replace x with -1
Just check it out now
P(x)=x^2+2x+1
P(-1)=(-1)^2+2(-1)+1
=1+(-2)+1
=0
5:09
Purple! I hated math in school (back in the 50's and 60's - crappy teachers made math boring/confusing) -- but I love solving puzzles and I've always been good with all the sciences (except for the math part that I have just always avoided). Anyway - watching your videos makes math seem fun and maybe it's not too late for me to start learning math at 70 years old?
Blue from the Philippines, how exciting!
I have discovered your videos recently, and I noticed you always detail how you get from (a+b)² to a²+2ab+b².
I don't know in your country, but in France we are taught what we call "identités remarquables" (remarkable identities) that we are supposed to know:
(a+b)² = a²+2ab+b²
(a-b)² = a²-2ab+b²
(a+b)(a-b) = a²-b²
I think he's from America, and we also learned those identities! I think he just prefers to show (basically) every step in these videos.
even in india
Apprendrez-moi le français(i say this to every french person)
It just speeds up the process knowing these identities, I guess Andy details every step for learning purposes
im only a 6th grader and this is fun and you explain it very well
Teal - Im slowly falling back in love for pure mathematics after being a pi=3 engineer for 10 years
I just plugged in 11 to start with figuring we had a 3/4/5 (6/8/10) triangle. Doing so makes the large triangle an 8 15 17 triangle. 17-11 = 6 which confirms the 6/8/10.
I did it sort of in my head when I realized there qas going to be an x^4 polynomial, and didnt even consider going further.
Purple, this was really good. It would be cool to have a test that's like one massive question like this.
except I realized there's a big issue if I'm wrong
Purple. Definitely a bit involved but seems fun, and tedious.
After I saw the triangle with c=10 I just knew x was either 9or 11 since you need legs 8 and 6 to get a hypotenuse of 10, and plugging in those two x values into x gives you 8 or 6
Blue. That was intense.
a variable a was chosen but a could actually be determined by using pythagorean theorem on the bigger triangle
Lilac is the most beautiful colour
Blue. That was some really tedious work. Good job.
Purple. I used to do math when I was stressed when I was a kid. This reminds me that times
Olive drab
I only just found your channel and your problems prove to be very fun to do as an activity
Green. I'm about to retake all my maths. I appreciate your videos.
Pink! This problem was a rollercoaster but so exciting!
At first sight the diagram reminded me of the proof for sine of summed angles
Purple, your videos are helping me see problems in different perspectives and I realized that they're not all that hard!
Blue, using synthetic division and the factor theorem would have probably made solving the polynomial much easier.
Green. This problem was ridiculous!
Purple. This felt like watching a magician keep pulling handkerchiefs out of their sleeve.
If f(3)=0 that means that the reminder of dividing f(x) by (x-3) is 0, f(a) is a reminder of dividing f(x) by (x-a).
mint! at that point where there are too many x inside the equation i would probably just look at the multiple option and try the answer one by one see which one is correct
Blue be like let's confuse them
Blue. And holy moly that was a slog all the way to the end.
Blue! This brings back lots of memories. What fun.
Blue, how exciting… and long! Worth the wait.
Sky blue! My daughter is doing this in her advanced 7th grade math class. I showed her this and she thought I was nuts for liking to watch this. 😂😂
Pretty sure you know from the beginning that x is 9 or 11 because the 10 hypotenus makes the first triangle a special right and the known side has to be 9 or 11. From there you take 9 and assume a is 8 or take 11 and assume a is 6. Then pothag the big triangle to check whether the hypotenuse equals x+6 or x+8
Earth tones suit me. How exciting!
Red, though I first worked through all the ways to use quadrilateral formulas. The other missing side length is non integer and made a hash of things. Doing the quadrilateral area formula against the sum of triangles became a mess. Discarding that I did as you dud in a more convoluted way. Rather than struggling through finding the roots of the quartic, I threw it into a spreadsheet, plotted and quickly solved it that way. Though not proper for this sort of solution, 50 years of engineering on - I use them a lot to bash through problems.
But then too, I tend to solve for all of the missing elements and nit just the one sought in the problem statement. Force of habit.
By the end I would have forget what I was looking for
Green. This was just awesome.
Light blue. You explained it nicely.
Purple. Love your videos!
You don't need to do long division and check the remainder when guessing roots. Just plug your guess into the polynomial and see if it is equal to 0.
Blue! Love this problem! How exciting! 💙
Blue. I love these videos. Reminding me of math I used to do so much faster!
Green.
Now I'm going to have to look up the proof to the RRT!
Brown. I am working all of your problems and getting maybe 2% close!
Every one of them, specially blue green, pistachio green and light orange
Blue, I couldn't stop watching you smashing these big numbers, that were supposed to destroy our will to live. Thank you for this.
Aluminium is my favourite material
Magenta. broooo wth was this. my brain visited cauldron of Ramanujan while solving XD
I'm honestly hook on educational RUclips now, it should literally be the only RUclips
Red and black are my favorite colors.
Green is just so beautiful
Blue. Where was these videos when I was about to take my exams? Anyways, love it!
Black green ❤
"turquoise" -thamy
Black, red, any type of blue (except skyblue), green, and
And grey.
Mint green is very pleasant
Fav colour is a deep emerald
Black and green I loved this interesting math problem
respect for writing all that
Pink. My guy, you are the reason i don't have an f in Geo rn.
mix between blue and green
Mirror glass green...geebus having to factor that polynomial...
My favorite color is blue, and my favorite mathematician is you
Royal Blue, nice
Yellow! And how exciting indeed!
The moment I saw 10cm, I immediately thought of 10,8,6 triangle, and hit and trial worked. Not a good way to solve, but kinda worked.
how exciting - blue
purple
and dear god, what a process
My favorite color is red... how exciting.
At the end you could have said "How Thrilling".
Purple!! That was intense
This was a really fun one. Favorite color is blue.
Teal! Despite being long and tedious you still managed to make it seem fun. How exciting!
Red. Ouch! How exciting indeed. It's been so long. Thank you
blue.
That was painful
Cerulean, can you do a video on polynomial long division?
Green. Thanks for reminding me how fun algebra can be 😀