If $x=\sqrt{{\sqrt{5}+1\over \sqrt{5}-1}}$ What is the value of $5x^2-5x-1?$ If $$x=\sqrt{{\sqrt{5}+1\over \sqrt{5}-1}}$$ What is the value of $5x^2-5x-1?$
Efforts: 
After rationalization, I got $x={\sqrt{5}+1\over 2}$ and $x^2={\sqrt{5}+1\over \sqrt{5}-1}$. Going by this method is very tedious and boring.
Is there a more clever and imaginative way to approach this problem?
Thanks.

You already have $x=\frac{\sqrt5+1}{2}$. Then $x^2=\frac{\sqrt5+3}{2}$ and so $x^2=x+1$.
Therefore $5x^2-5x-1=5x+5-5x-1=4.$
