Question

Solve the following equation by factorisation :

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

Answer 1

`sqrt(x + 15) = x + 3`
Squaring on both sides
x + 15 = (x + 3)² 
⇒ x² + 6x + 9 – x – 15 = 0
⇒ x² + 5x – 6 = 0
⇒ x² + 6x – x – 6 = 0
⇒ x(x + 6) –1(x + 6) = 0
⇒ (x + 6)(x – 1) = 0
Either x + 6 = 0,
then x = -6
or
x – 1 = 0,
then x = 1
∴ x = –6, 1
Check :
(i) If x = –6 then
L.H.S. = `sqrt(x + 15)`
= `sqrt(-6 + 15)`
= `sqrt(9)`
= 3
R.H.S. = x + 3
= –6 + 3
= –3
∵ L.H.S. ≠ R.H.S.
∴ x = –6 is not a root
(ii) If x = 1, then
L.H.S. - `sqrt(x + 15)`
= `sqrt(1 + 15)`
= `sqrt(16)`
= 4
R.H.S. = x + 3
= 1 + 3
= 4
∵ L.H.S. = R.H.S.
∴ x = 1 is a root of this equation
Hence x = 1.