Question

Solve. (x + 3)^1/2– 1 = x

Answer 1

x=1

Explanation:

`(x + 3) ^{ (1)/(2) } - 1 = x \\ √(x + 3) - 1 = x \\ √(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`