Question

Is the solution of √x−3+√x=3 extraneous?

Answer 1

$\sqrt{x - 3} + \sqrt{x} = 3 \\ \\ \sqrt{x - 3} = 3 - \sqrt{x} \\ \\ sobs \\ \\ x - 3 = 9 + x - 6 \sqrt{x} \\ \\ \sqrt{x} = 2 \\ \\ x = 4$

hope it helps

Answer 2

$\sqrt{x - 3} + \sqrt{x} = 3 \\ \\ \sqrt{x - 3} = 3 - \sqrt{x} \\ \\ squaring \: on \: both \: sides \\ \\ x - 3 = 9 + x - 6 \sqrt{x} \\ \\ 6 \sqrt{x} = 12 \\ \\ \sqrt{x} = 2 \\ \\ squaring \\ \\ x = 4$

hope it helps