Question

Solve. (x + 3)^1/2– 1 = x

Answer 1

Answer:

x=1

Step-by-step explanation:

$(x + 3) ^{ \frac{1}{2} } - 1 = x \\ \sqrt{x + 3} - 1 = x \\ \sqrt{x + 3} = x + 1 \\ square \: both \: sides \\ x + 3 = {x}^{2} + 2x + 1 \\ {x}^{2} + 2x - x + 1 - 3 = 0 \\ {x}^{2} + x - 2 = 0 \\ x ^{2} + 2x - x - 2 = 0 \\ (x^{2} + 2x) - (x + 2) = 0 \\ x(x + 2) - 1( x + 2) = 0 \\ (x - 1)(x + 2) = 0 \\ x - 1 = 0 \\ x = 1 \\ \\ \\ x + 2 = 0 \\ x = - 2$