Question

Solve the following equation by factorization:

`sqrt(3x^2 - 2) = (2x - 1)`

Answer 1

Given,

⇒ `sqrt(3x^2 - 2) = (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}.