Question

Find the roots of the quadratic equation $3x^2-2\sqrt{6}x+2=0$.

Answer 1

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

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

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

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

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

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

$\therefore$ the roots are $\{\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}}\}$