Question
Solve the following quadratic equation by factorization.
$3 x^2-2 \sqrt{6} x+2=0$
$3 x^2-2 \sqrt{6} x+2=0$
✓
Answer
$3 x^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$
$\Rightarrow(\sqrt{3} x-\sqrt{2})=0 \text { or }(\sqrt{3} x-\sqrt{2})=0$
$ x=\frac{\sqrt{2}}{\sqrt{3}} \text { or } x=\frac{\sqrt{2}}{\sqrt{3}}$
$ \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$
$\Rightarrow(\sqrt{3} x-\sqrt{2})=0 \text { or }(\sqrt{3} x-\sqrt{2})=0$
$ x=\frac{\sqrt{2}}{\sqrt{3}} \text { or } x=\frac{\sqrt{2}}{\sqrt{3}}$
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