Solve the following quadratic equation: 3x^2-2 2x-2 3=0 - Vidyadip

Question

Solve the following quadratic equation:$\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$

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Answer

$\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$$\Rightarrow\sqrt{3}\text{x}^2-3\sqrt2\text{x}-\sqrt{2}\text{x}-2\sqrt{3}=0$
$\Rightarrow\sqrt3\text{x}\big(\text{x}-\sqrt6\big)-\sqrt2\big(\text{x}-\sqrt6\big)=0$
$\Rightarrow\big(\text{x}-\sqrt6\big)\big(\sqrt3\text{x}+\sqrt2\big)=0$
$\Rightarrow\text{x}-\sqrt6=0$ or $\sqrt{3}\text{x}+\sqrt2=0$
$\Rightarrow\text{x}=\sqrt{6}$ or $\text{x}=\frac{-\sqrt{2}}{\sqrt{3}}$

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