This Equation Looks Impossible Until You Notice One Thing
Автор: NonsoMaths
Загружено: 2026-02-12
Просмотров: 343
Описание:
In this tutorial, I solve the unique equation (x⁴ - 13x² + 36)⁴ + √(x³ - 7x + 6) = 0 for real x using a clever observation rather than brute force. I show you how to recognize that since the first term is always nonnegative thanks to the even exponent, and the square root term is also nonnegative by definition, the sum can only be zero when both terms are zero simultaneously. This transforms a seemingly impossible equation into solving two simpler equations: a quadratic in disguise (x⁴ - 13x² + 36 = 0) and a cubic (x³ - 7x + 6 = 0). We then factor, find the intersection of solution sets, and check the domain for the square root. This is a fantastic problem for precalculus and algebra students, teaching a powerful reasoning shortcut that saves time on tests and competitions.
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#matholympiad #maths #algebra
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