Dislike for such a clickbait... I wanted to see the solution for 2^x + 4^x = 9^x, but found another much simpler problem

X can be any degree 2.

also x ~= 1.02239294

Not OR but AND

X can be 2

Bring one side to an algebraic format and make the other side equivalent to it. Good technique!

So easy but too long

Your joking i assume

Seems like a lot of unnecessary steps I looked at it and got the answer

This is at least 2 times longer than it needs to be maybe even 3 times. You could have rearranged 1 and subbed directly into 2 and solved the resulting quadratic from there.

I know you like to carefully write with your bran new pen BUT you should not rewrite the question and skip the trivial developments... Boring

yeah, same as other people. thumb down for misleading title.

You receive a thumbs down for the "misleading title". Thus is a math problem for grade 8, and your solution is very well detailed, I'd say detailed enough such that any average 7th grade student understands what you did. A suitable title for your post is "Can you solve this 8th-grade math question in a way that a 7th grade understands what you did?"👎👎👎

from your equation (3), xy = -15, then by inspection x = 5, y = -3 and x = -3, y = 5.

Definitely NOT Maths Olympiad question. It's 8th grade maths. And much simpler solution can be used.

I gave a thumbs down, not for the content (which I didn't even view), but for the misleading title containing "math olympiad". Anyone who have already learned Vieta's formulas in the school (8th grade) knows how to solve this.

Why take such a circuitous route, deriving xy=-15, and then refactoring to (x+3)(x-5)=0? Wouldn't it be more straightforward to just substitute y=2-x into the second equation giving x^2 + (2-x)^2 = 34 which simplifies directly to x^2 - 2x -15 = 0 and then use the roots of a quadratic equation formula from there?

If you simply expand the fraction with three you get this answer at once! But there is still a third root, so is that really simpler? Or is this once again 6:36 min of bullshit?

7! I can mentally solve it using brute force, noticing that 10 x 9 x 8 = 720 = 6! Therefore 10 x 9 x 8 x 7! = 10! = 6! x 7!

Engineer's solution: x = 1 8 + 1 = 10 : close enough!

7*8*9*10!=7! 7 cannot be breaked and and according to the the problem, 7*8*9*10 is possible to be expressed in factorial.Hence the 7*8*9*10 will end as follows 1*2*3*4*5*7. No calculation required and speedy mental math here can adduce the answer. Comment please

Don't understand what the first three minutes of the video is for with all those extra useless steps since it is obvious that x! equals 7 * 8 * 9 * 10. That would have been my starting point. Showing that this equals 7! is very clever however.

ooommmgggg 😂

Great 👍

33 wins!

with calculator take only few second by using a^x = b => x = (logb)/loga . which b =V{16(V8)} ; a= 64 . Yield x =.458

x = .458

You didn't solved the equation given in the teaser picture...

Very easy. For everyone who knows complex numbers. This kind of equation is taught in high school. And you lost a lot of time making division. When you counted discriminant b^2-4ac = (-6)^2-4*1*36 we can notice it's 36 - 4*36 so we can take out 36 outside the bracket: 36 * (1 - 4) = 36*(-3). Square root is immediately 6*sqrt(3) i

Your solution is little bit longer Consider equation X2-sX+p=0

Your sum and product is equal to 9 or 19?

The two solutions are really just one solution, whichever value you decide to call "x" or "y" is irrelevant here.

Решил по формуле Пика за 3 секунды

y = 6-x so xy = x(6-x). Therefore x(6-x) = 36. That gives x^2 - 6x + 36 = 0, Solve using the quadratic fromula: x = ( 6 ± √(36 - 4*36) ) / 2 = ( 6 ± √( - 3*36) ) / 2 = ( 6 ± 6i√3 ) / 2 = 3 ± 3i√3. Since the equations are symmetrical in x and y, these must be the conjugate solutions for y, hence y = 3 ∓ 3i√3. That is mainly mental arithmetic and doesn't take 9 minutes. Was it the Toytown Math Olympiad?

2

2⁹⁸

If you put root(x)=y root(5) Then you can get that equation 3-y=y-1 》》y=2 , Don't make math hard

It's too long way

V2-1.

👍👍👍🤪👋

That's the difference between following a script and understanding.

2^x=2, x=1, trivial by guessing as well

Oups ! I just compute that both (½(-1-i√3))³=1 and (½(-1+i√3))³=1. So these two complex values are not solution of the x³-8=0 equation ! I expected that the three solutions of the equation x³-8=0 are { 2 ; -1+i√3 ; -1-i√3}. You may have made a mistake at the very end of your very long long algebraic fairway. Try to be more efficient in algebraic expression manipulations. You may understand that only teachers are decomposing so much each step: it is just for educational purposes. The mathematician's practices lead them to a more concise and efficient notation's handling. And don't forget to always check your results

The complex solutions are -1+-i√3