Solve : x⁴ - 2x² - 3 = 0

Question

KnowledgeBoat · Accepted Answer

Let x² = y, ⇒ x⁴ - 2x² - 3 = 0 ⇒ y² - 2y - 3 = 0 ⇒ y² - 3y + y - 3 = 0 ⇒ y(y - 3) + 1(y - 3) = 0 ⇒ (y + 1)(y - 3) = 0 ⇒ y + 1 = 0 or y - 3 = 0 [Zero product rule] ⇒ y = -1 or y = 3 ∴ x² = -1 or x² = 3 Since, square of a number cannot be negative, ∴ x² = 3 ⇒ x = Hence, x = +1.73, -1.73.

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