Question

One of the roots of the quadratic equation $x^2+2\sqrt{2x}-16=0$ is

• A. $\sqrt{2}$
• B. $3\sqrt{2}$
• C. $4\sqrt{2}$
• D. $2\sqrt{2}$

Answer 1

The correct option is D $2\sqrt{2}$

Cinsider the equation,
$x^2+2\sqrt{2x}-16=0$
$\Rightarrow x^2+4\sqrt{2x}-2\sqrt{2x}-16=0$
$\Rightarrow x(x+4\sqrt{2})-2\sqrt{2}(x+4\sqrt{2})=0$
$\Rightarrow (x+4\sqrt{2}(x-2\sqrt{2})=0$
$\Rightarrow x+4\sqrt{2}=0orx-2\sqrt{2}=0$
$\Rightarrow x=-4\sqrt{2}orx=2\sqrt{2}$
Hence, the correct answer is option (4).