Giant Powers Vanish in Seconds With This Olympiad Factoring Trick | Find x

Описание: Math Olympiad Challenge — Massive Powers That Secretly Simplify!

(x⁸ - x²)/(x⁴ - x²) = 9 → Find ALL real values of x

When most students see x⁸ and x⁴ in the same
fraction, they immediately reach for a calculator
or try to expand everything — leading to an
absolute disaster.

But this problem was DESIGNED to be factored.

Step by step, two incredibly clean cancellations
wipe away those terrifying powers — first an x²
disappears, then (x²-1) vanishes using a difference
of cubes identity — until you're left with a simple
quadratic in disguise.

The result is one of the most satisfying chains
of simplification in all of competition algebra.

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🧠 What You'll Learn:
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✔️ How to factor x²(x⁶-1) and x²(x²-1) to cancel x²
✔️ Why x⁶-1 = (x²-1)(x⁴+x²+1) using difference of cubes
✔️ How both massive cancellations reduce the equation
to just x⁴ + x² + 1 = 9
✔️ The classic substitution y = x² that reveals the quadratic
✔️ How to apply the quadratic formula to get √33 answer
✔️ Why the negative root is rejected for real solutions
✔️ Why x = ±√((-1±√33)/2) is the elegant Olympiad answer

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📌 Try It Yourself First!
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Pause before the solution — can you spot
BOTH cancellations before watching?
Drop your approach in the comments!
Did you find both values of x? 👇

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