If $$ x = \sqrt{\frac{\sqrt{5} + 1}{\sqrt{5} - 1}}$$, then the value of $$5x^2 - 5x -1 $$ is

Given : $$ x = \sqrt{\frac{\sqrt{5} + 1}{\sqrt{5} - 1}}$$

=> $$ x = \sqrt{\frac{\sqrt{5} + 1}{\sqrt{5} - 1}\times (\frac{\sqrt5+1}{\sqrt5+1})}$$

=> $$x=\sqrt{\frac{(\sqrt5+1)^2}{5-1}}$$

=> $$x=\frac{\sqrt5+1}{2}$$ --------------(i)

Squaring both sides, we get : $$x^2=\frac{6+2\sqrt5}{4}$$ --------------(ii)

To find : $$5x^2 - 5x -1 $$

= $$5(x^2-x)-1$$

Substituting values from equations (i) and (ii), we get :

= $$5[(\frac{6+2\sqrt5}{4})-(\frac{\sqrt5+1}{2})]-1$$

= $$5\times(\frac{6+2\sqrt5-2\sqrt5-2}{4})-1$$

= $$5\times1-1=4$$

=> Ans - (C)