Can You Solve This Symmetric Polynomial Equation?

Can you find x from this elegant equation?
Solve: (1 + x²)(1 + x⁴) = 4x³, Find x
This problem features a product of two binomials equaling a monomial, which looks tricky to solve! But there's a strategic approach: expand the left side to get 1 + x² + x⁴ + x⁶ = 4x³, then rearrange into a polynomial equation. The key is recognizing patterns or using substitution like y = x² to transform this into a manageable cubic equation.
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This problem teaches you:
✓ Polynomial expansion and rearrangement
✓ Strategic substitution techniques
✓ Solving higher-degree equations
✓ Pattern recognition in symmetric forms
✓ Algebraic manipulation skills
Perfect for students preparing for:
• Math Olympiads IMO, AMC, AIME
• Competition mathematics
• Advanced Algebra courses
• Anyone who loves polynomial equations!
The solution requires careful algebraic work but yields clean solutions!
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