Question

What is the solution of sqrt x+12=x ? x = –3 x = 4 x = –3 or x = 4 no solution

Answer 1

\left[x _{2}\right] = \left[ 4\right][x​2​​]=[4] totally value

Answer 2

x = 4 is the solution

given $\sqrt{x+12}$ = x ( square both sides )

x + 12 = x² ( rearrange into standard form )

x² - x - 12 = 0 ← in standard form

(x - 4 )(x + 3 ) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

substitute these values into the original equation and if both sides are equal then they are the solutions

x = 4 : $\sqrt{4+12}$ = $\sqrt{16}$ = 4 = x ← correct

x = - 3 : $\sqrt{-3+12}$ = $\sqrt{9}$ = 3 ≠ - 3 ← false

the solution is x = 4