Germany || Can You Solve This? || A Very Nice Math Olympiad Problem

In this video, I'll be showing you step by step on how to solve this Exponential problem using a simple trick.
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[@shannonmcdonald7584]

Factor when ever you can. Good idea to start solving.

[@paulortega5317]

The equation reduces down to (x² + 1 + 1/x²) / (x + 1 + 1/x) = 3
Let u = x + 1 + 1/x
u² = (x + 1 + 1/x)² = (x² + 1 + 1/x²) + 2(x + 1 + 1/x) = (x² + 1 + 1/x²) + 2u
u² - 2u = (x² + 1 + 1/x²)
The equation (x² + 1 + 1/x²) / (x + 1 + 1/x) = 3 becomes (u² - 2u) / u = 3
u = 5
x + 1 + 1/x = 5
x² - 4x + 1 = 0
x = 2 ± √3

[@SpencersAcademy]

Superb! 👏

[@RealQinnMalloryu4]

{x^9+x^9 ➖ }=x^18 {x^7+x^7 ➖}=x^14 {x^18+x14}=x^32 {x^5+x^5 ➖}=x^10 {x^32+x^10}=x^42 /{x^8+x^8 ➖}=x^32 {x^7+x^7 ➖}= x^14 {x^32+14}=x^46 {x^6+x^6 ➖}=x^12 {x^46+x^12}=x^58 x^42/x^58=x,^6^7/x2^29 x^6^7^1/x^2^29^1 x^6^1^1/2^1^1 x^3^2/x^2^1 x^3^1/x^2^1 x^3/x^2 (x ➖ 3x+2). 3^29/29^1 3^29^1/1^1 3^1^1 3^1 (x ➖ 3x+1).
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