Question

\sqrt{x} +12=x?\\
what is the solution
-3
4
-3 and 4
no solution

Answer 1

x = 4

Explanation:

given

`√(x+12)` = x ( square both sides )

(
`√(x+12)`)² = x²

x + 12 = x² ( subtract x + 12 from both sides )

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

As a check

substitute these values into the equation and if the left side equals the right side then they are the solutions

x = 4 :
`√(12+4)` =
`√(16)` = 4 = right side

x = - 3 :
`√(-3+12)` =
`√(9)` = 3 ≠ - 3

The only valid solution is x = 4