Solve : 2x⁴ - 5x² + 3 = 0

Question

KnowledgeBoat · Accepted Answer

Let x² = y, ⇒ 2x⁴ - 5x² + 3 = 0 ⇒ 2y² - 5y + 3 = 0 ⇒ 2y² - 2y - 3y + 3 = 0 ⇒ 2y(y - 1) - 3(y - 1) = 0 ⇒ (2y - 3)(y - 1) = 0 ⇒ 2y - 3 = 0 or y - 1 = 0 [Zero product rule] ⇒ 2y = 3 or y = 1 ⇒ y = or y = 1. ∴ x² = or x² = 1 ⇒ x = or x = Hence, x = +1.22, -1.22, +1, -1.

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