Question

Find the value of c
$\frac{c}{ \sqrt{c ^{2} - 4 } } = \sqrt{3}$
​

Answer 1

Answer

$\sf \frac{c}{ \sqrt{c ^{2} - 4 } } = \sqrt{3}$

⟹ $\sf c = \sqrt{3} \times \sqrt{ {c}^{2} - 4}$

⟹ $\sf c = \sqrt{3( {c}^{2} - 4)}$

⟹ $\sf c = \sqrt{3 {c}^{2} - 12}$

Squaring both the side :-

⟹ $\sf {c}^{2} = 3 {c}^{2} - 12$

⟹ $\sf 3 {c}^{2} - {c}^{2} = 12$

⟹ $\sf 2 {c}^{2} = 12$

⟹ $\sf {c}^{2} = \frac{12}{2}$

⟹ $\sf {c}^{2} = 6$

⟹ $\boxed{\sf c = \sqrt{6}}$