Prove that $\displaystyle \frac{2-\sqrt{3}}{5}$ is an irrational number, given that $\displaystyle \sqrt{3}$ is an irrational number.

Assuming \(\displaystyle \frac{2-\sqrt{3}}{5}\) to be a rational number. \[\begin{aligned} & \Rightarrow \frac{2-\sqrt{3}}{5}=\frac{p}{q}, u \\ & \Rightarrow \sqrt{3}=\frac{2 q-5 p}{q} \end{aligned} \] Here RHS is rational but LHS is irrational. Therefore our assumption is wrong. Hence \(\displaystyle \frac{2-\sqrt{3}}{5}\) is an irrational number.