ฝัง
- เผยแพร่เมื่อ 5 ก.ค. 2024
- Chinese | Math Olympiad | Can You Solve ?
Welcome to another exciting math challenge! In this video, we tackle a difficult algebra problem from the Chinese Math Olympiad. This problem is sure to test your problem-solving skills and mathematical prowess.
Are you up for the challenge? Watch the video, try to solve it on your own, and then see if your solution matches ours. Don't forget to comment below with your approach and solution!
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🔢 What You'll Learn:
Key strategies for simplifying complex expressions
Tips and tricks to approach difficult simplification problems
Step-by-step walkthrough of the solution
🧠 Challenge Yourself:
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Thanks for Watching !
Interesting proof.
(9^60+1)/9^ 30
9^30+1/9^30=1+9^60/9^30
Nice solution, but it was not necessary to divide by 3 at first place.
I agree with you. Just squaring both sides.
Synthetic division is much easier since we only need to find x-x0= 0; to reduce all higher order polynomial to zero order.
Here we only need to solve 9x+1/3x=sqrt(6) to obtain x0 =sqrt(6)*(1 +/- i )/18. Here x^40 -> remainder (x^40 /(x-x0)) .
This gives= x^40 = 2.3590e-29 => (1 /x^40) = 4.2391e+28 -> (x^40 +1/x^40) = 4.2391e+28+ 2.3590e-29 ~4.2391e+28
More straightforward solution is to calculate x1,2 = (sqrt(6)/180. (1 +- i). Then (1 +-i)^4=4 !!! This eliminates i.
Hello
Sir
A faster method? 9x+1/3x=6^(1/2)=> x=(sqrt(6)/18)*(1+/- i) =(sqrt(3)/9)*exp(i*pi/4) =>x^40=(1/9^30)exp(i*10pi).
=> x^40 +1/x^40 = (1/9)^30 +9^30 ~> 9^30 ~> 4.2391e+28.
[9^(30)]+[9^(-30)]
It was a wonderful explanation and a nice solution 👍🏻 🙏
Or let u = 3*sqrt(3)*x
u + 1/u = sqrt(2)
u^2 + 1/u^2= 0
u^4 = -1
x^4 = -1*3^-6
x^40 = 3^-60
18x^2+2/6x^2 =20x^2/6x^2 =3.2x (x ➖ 3x+2) x^80+2/x80 =2/x^160 =x^80 2^30 2^40 2^40 2^5^4 2^5^14 2^1^14 2^4 2^2^2 1^1^2 1^2 (x ➖ 2x+1)