Question

The sum of the solutions of the equation $\left|\sqrt{x}-2\right|+\sqrt{x}\left(\sqrt{x}-4\right)+2=0, \left(x>0\right) $ is equal to:

• A. 4
• B. 9
• C. 10
• D. 12

Answer 1

Answer: (C)

$\left|\sqrt{x}-2\right|+\sqrt{x}\left(\sqrt{x}-4\right)+2=0 $
$ \left|\sqrt{x}-2\right|+\left(\sqrt{x}\right)^{2} -4\sqrt{x}+2=0$
$ \left|\sqrt{x} - 2\right|^{2} + \left|\sqrt{x}-2\right|-2=0$
$ \left|\sqrt{x}-2\right| = -2$ (not possible) or $ \left|\sqrt{x} -2\right| = 1 $
$ \sqrt{x}-2= 1,-1 $
$ \sqrt{x} =3, 1 $
$ x =9, 1 $
Sum = $10$