136
Prove that $\frac{\sqrt{3}+5}{2}$ is an irrational number, where it is given that $\sqrt{3}$ is irrational.
Show SolutionHide Solution↓
Let $\frac{\sqrt{3}+5}{2} = a$, where '$a$' is a rational number
$\implies \sqrt{3} = 2a - 5$
Here LHS is an irrational number but RHS is a rational number
So, our assumption is wrong
Hence, $\frac{\sqrt{3}+5}{2}$ is an irrational number
$\implies \sqrt{3} = 2a - 5$
Here LHS is an irrational number but RHS is a rational number
So, our assumption is wrong
Hence, $\frac{\sqrt{3}+5}{2}$ is an irrational number