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
$\begin{array}{l}3 x^2-\sqrt{6} x-\sqrt{6} x+2=0 \\ \Rightarrow \sqrt{3} x(\sqrt{3} x-\sqrt{2})-\sqrt{2}(\sqrt{3} x-\sqrt{2})=0 \\ \Rightarrow(\sqrt{3} x-\sqrt{2})(\sqrt{3} x-\sqrt{2})=0 \\ \Rightarrow(\sqrt{3} x-\sqrt{2})=0 \text { or }(\sqrt{3} x-\sqrt{2})=0 \\ x=\frac{\sqrt{2}}{\sqrt{3}} \text { or } x=\frac{\sqrt{2}}{\sqrt{3}}\end{array}$
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