Question

Solve the following quadratic equation by factorization.
$3x^2-2\sqrt{6x}+2=0$

Answer 1

$3x^2-2\sqrt{6x}+2=0$

$\Rightarrow 3x^2-\sqrt{6}x-\sqrt{6}x+2=0$

$\Rightarrow \sqrt{3}x(\sqrt{3}x-\sqrt{2})-\sqrt{2}(\sqrt{3}x-\sqrt{2})=0$

$\Rightarrow (\sqrt{3}x-\sqrt{2})(\sqrt{3}x-\sqrt{2})=0$

$\Rightarrow x=\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}}$