Question
Solve the following quadratic equation:$3\text{x}^2-2\sqrt6\text{x}+2=0$
✓
Answer
$3\text{x}^2-2\sqrt6\text{x}+2=0$$\Rightarrow3\text{x}^2-\sqrt6\text{x}-\sqrt6\text{x}+2=0$
$\Rightarrow\sqrt3\text{x}\big(\sqrt3\text{x}-\sqrt2\big)-\sqrt2\big(\sqrt3\text{x}-\sqrt2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}-\sqrt2\big)\big(\sqrt3\text{x}-\sqrt2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}-\sqrt2\big)^2=0$
$\Rightarrow\sqrt3\text{x}-\sqrt2=0$
$\Rightarrow\text{x}=\frac{\sqrt2}{\sqrt3}$ (repeated root)
$\Rightarrow\sqrt3\text{x}\big(\sqrt3\text{x}-\sqrt2\big)-\sqrt2\big(\sqrt3\text{x}-\sqrt2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}-\sqrt2\big)\big(\sqrt3\text{x}-\sqrt2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}-\sqrt2\big)^2=0$
$\Rightarrow\sqrt3\text{x}-\sqrt2=0$
$\Rightarrow\text{x}=\frac{\sqrt2}{\sqrt3}$ (repeated root)
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