Question

Solve the following equation by factorization:

`sqrt(3x^2 + x + 5) = (x - 3)`

Answer 1

Given,

⇒ `sqrt(3x^2 + x + 5) = (x - 3)`

Squaring both sides we get:

⇒ (3x² + x + 5) = (x – 3)²

⇒ 3x² + x + 5 = (x²) + (3²) – 2 × x × 3

⇒ 3x² + x + 5 = x² + 9 – 6x

⇒ 3x² + x + 5 – x² – 9 + 6x = 0

⇒ 2x² + 7x – 4 = 0

⇒ 2x² – x + 8x – 4 = 0

⇒ x(2x – 1) + 4(2x – 1) = 0

⇒ (2x – 1)(x + 4) = 0

⇒ (2x – 1) = 0 or (x + 4) = 0   ...[Using zero-product rule]

⇒ 2x = 1 or x = –4

⇒ x = `1/2` or x = –4

Hence, `x = {-4, 1/2}`.