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An Engaging Algebra Simplification | Math Olympiad
Рет қаралды 2,242
Ай бұрынAn Engaging Algebra Simplification | Math Olympiad
Welcome to another exciting math challenge! In this video, we dive into an engaging algebra simplification problem that is perfect for Math Olympiad preparation. This problem will test your algebraic skills and problem-solving abilities. Whether you're a student preparing for math competitions or a math enthusiast looking for a stimulating challenge, this video is for you.
Don't forget to pause the video and try solving the problem on your own before watching the solution. Let's see if you can evaluate it!
🔢 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:
Pause the video, try to solve the problem on your own, and then watch as we break down the solution. Share your approach and answers in the comments below!
👍 Don't Forget to:
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4. Join us and enhance your problem-solving skills. Can you master this simplification problem?
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Thanks for Watching !
@mohammedsaysrashid3587 Ай бұрын
It was a wonderful introduction and clearly explained...thanks Sir for sharing 🙏.....E = 134671/9
@johnstanley5692 Ай бұрын
x^2-2*x-93=0>x= -1/2 +/-sqrt(373)/2. define Z(1) =(x-9)/sqrt(3) + sqrt(3)/(x-9). (where Z(n) = (Y)^n +1/(Y)^n ). Now use standard recursion for Z(n), i.e. Z(n+1)= Z(n)Z(1) - Z(n-1) & Z(2n) = Z(n)^2-2. Here only need the doubling formula. i.e. Z(2n) = Z(n)^2-2. Here Z(1) = sqrt(1119)/3 => Z(2)= Z(1)^2-2 = 367/3 => Z(4) = Z(2)^2 -2 = 134671/9
@user-kp2rd5qv8g Ай бұрын
If x-9=t, x =t+9. Thus, t+9 -93/(t+9) = -1 > t-3/t = -19 > t/(sqrt3) - (sqrt3)/t = -19/sqrt(3) > t^2/3+3/t^2 = 367/3 > t^4/9 + 9/t^4 = (367/3)^2 - 2 > The required expression is 134671/9.
@abcekkdo3749 Ай бұрын
E=134671/9
@RealQinnMalloryu4 Ай бұрын
(x)^2 ➖ 93/(x)^2= {x^2 ➖ 93}/x^2 =91/x^2 =92^ 62^31 2^31^31^1 2^31^1 1^1 2^1^1 2^1 (x ➖ 2x+1). { 6561x^4/9+ 9/6561x^4 } {6570x^4/6570x^4} =1x^1 (x ➖ 1x+1).
@SidneiMV Ай бұрын
x - 9 = u => x = u + 9 E = u⁴/9 + 9/u⁴ = (u/√3)⁴ + (√3/u)⁴ u + 9 - 93/(u + 9) = -1 (u + 9)² + (u + 9) - 93 = 0 u² + 18u + 81 + u + 9 - 93 = 0 u² + 19u - 3 = 0 (u² + 19u - 3)/(u√3) = 0 u/√3 + 19/√3 - √3/u = 0 u/√3 - √3/u = -19/√3 (u/√3)² + (√3/u)² = 19²/3 + 2 (u/√3)⁴ + (√3/u)⁴ = (19²/3 + 2)² - 2 E = (19²/3 + 2)² - 2 E = 19⁴/9 + (4)19²/3 + 2 *E = (19⁴ + (12)19² + 18)/9* *E = 134671/9*
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