Question

\sqrt{x + 3} = x + 1​

Answer 1

$\sqrt{x+3} = x + 1  \\(\sqrt{x+3})^2 = (x + 1)^2\\x + 3 = x^2 + 2*x*1 + 1^2\\x + 3 = x^2 + 2x + 1\\x^2 + 2x + 1 - x - 3 = 0\\x^2 + x - 2 = 0\\\\D = b^2 - 4ac\\D = 1^2 - 4*1*(-2)\\D = 1 +  8\\D = 9\\\\x = (-b +- \sqrt{D}) / 2a\\x = (-1 +- \sqrt{9}) / 2\\x = (-1 +-3)/2\\x' = (-1 - 3)/2 = -2\\x'' = (-1 + \sqrt{9}) / 2\\x'' = (-1 + 3}) / 2\\x'' = 2/2 = 1$

x = 1