Question

Solve the following equation by factorization:

`sqrt(x + 15) + (x + 3)`

Answer 1

Given,

⇒ `sqrt(x + 15) + (x + 3)`

Squaring both sides, we get:

⇒ (x + 15) = (x + 3)²

⇒ x + 15 = (x)² + (3)² + 2 × x × 3

⇒ x + 15 = x² + 9 + 6x

⇒ x² + 9 + 6x – x – 15 = 0

⇒ x² + 5x – 6 = 0

⇒ x² + 6x – x – 6 = 0

⇒ x(x + 6) – 1(x + 6) = 0

⇒ (x + 6)(x – 1) = 0

⇒ (x + 6) = 0 or (x – 1) = 0   ...[Using zero-product rule]

⇒ x = –6 or x = 1

Substituting x = –6 in the L.H.S. of this equation `sqrt(x + 15)​ = (x + 3)`

⇒ `sqrt(-6 + 15)`

⇒ `sqrt(9)`

⇒ 3

Substituting x = –6 in the R.H.S. of this equation `sqrt(x + 15)​ = (x + 3)`

⇒ x + 3

⇒ –6 + 3

⇒ –3

L.H.S ≠ R.H.S.

∴ x = –6 is not valid.

Hence, x = {1}.