Can You Solve This Rational Equation with Two Roots?
Автор: Math Hacks Hub
Загружено: 2026-01-08
Просмотров: 339
Can you find x from this challenging equation?
Solve: x^(1/4) + x^(1/12) = 10, Find x
This problem combines fourth roots and twelfth roots equaling 10, which looks incredibly difficult! But there's a powerful substitution technique using the LCM of the exponents. The key is recognizing that 1/4 and 1/12 have LCM = 1/12, so let y = x^(1/12). This transforms the equation into y³ + y = 10, a much simpler cubic equation.
💡 Pause and try solving it before watching!
This problem teaches you:
✓ Fractional exponent equations
✓ Strategic substitution methods
✓ LCM of exponents approach
✓ Cubic equation solving
✓ Working with multiple root types
Perfect for students preparing for:
• Math Olympiads IMO, AMC, AIME
• Competition mathematics
• Algebra II and Pre-Calculus courses
• Anyone who loves challenging algebra!
The solution requires clever substitution but yields a surprisingly clean answer!
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#matholympiad #mathematics #algebra #fractionalexponents #substitution #exponents #problemsolving #mathchallenge #competitionmath #mathpuzzle #stem #precalculus
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