Question
Solve: $\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$
✓
Answer
$\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$$\Rightarrow\sqrt3\text{x}^2-3\sqrt2\text{x}+\sqrt2\text{x}-2\sqrt3=0$
$\Rightarrow\sqrt3\text{x}\big(\text{x}-\sqrt6\big)+\sqrt2\big(\text{x}-\sqrt6\big)=0$
$\Rightarrow\big(\sqrt3\text{x}+\sqrt2\big)\big(\text{x}-\sqrt6\big)=0$
$\Rightarrow\sqrt3\text{x}+\sqrt2$ or $\text{x}-\sqrt6$
$\Rightarrow\text{x}=\frac{-\sqrt2}{\sqrt3}$ or $\text{x}=\sqrt6$
$\Rightarrow\sqrt3\text{x}\big(\text{x}-\sqrt6\big)+\sqrt2\big(\text{x}-\sqrt6\big)=0$
$\Rightarrow\big(\sqrt3\text{x}+\sqrt2\big)\big(\text{x}-\sqrt6\big)=0$
$\Rightarrow\sqrt3\text{x}+\sqrt2$ or $\text{x}-\sqrt6$
$\Rightarrow\text{x}=\frac{-\sqrt2}{\sqrt3}$ or $\text{x}=\sqrt6$
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