Solve the following equation by factorization: √3x^2-2 = (2x - 1)

Question

KnowledgeBoat · Accepted Answer

Given, ⇒ = (2x - 1) Squaring both sides we get : ⇒ (3x2 - 2) = (2x - 1)2 ⇒ 3x2 - 2 = (2x)2 + (1)2 - 2 × 2x × 1 ⇒ 3x2 - 2 = 4x2 + 1 - 4x ⇒ 4x2 + 1 - 4x - 3x2 + 2 = 0 ⇒ x2 - 4x + 3 = 0 ⇒ x2 - x - 3x + 3 = 0 ⇒ x(x - 1) - 3(x - 1) = 0 ⇒ (x - 1)(x - 3) = 0 ⇒ (x - 1) = 0 or (x - 3) = 0 [Using Zero-product rule] ⇒ x = 1 or x = 3. Hence, x = {1, 3}.

Mathematics

Solve the following equation by factorization: √3x^2-2 = (2x - 1)

Quadratic Equations

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