Question

Short-Answer Questions

Solve: $\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$ [CBSE 2014]

Answer 1

$$\begin{gathered} \sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0 \\ \Rightarrow \sqrt{3}{x}^2-3\sqrt{2}x+\sqrt{2}x-2\sqrt{3}=0 \\ \Rightarrow \sqrt{3}x\left(x-\sqrt{6}\right)+\sqrt{2}\left(x-\sqrt{6}\right)=0 \\ \Rightarrow \left(x-\sqrt{6}\right)\left(\sqrt{3}x+\sqrt{2}\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x-\sqrt{6}=0\mathrm{or}\sqrt{3}x+\sqrt{2}=0 \\ \Rightarrow x=\sqrt{6}\mathrm{or}x=-\frac{\sqrt{2}}{\sqrt{3}}=-\frac{\sqrt{6}}{3} \end{gathered}$$

Hence, $\sqrt{6}$ and $-\frac{\sqrt{6}}{3}$ are the roots of the given equation.