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 = $10$