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.

Rationalizing the denominator of $x$, we get
$$x=\sqrt{\frac{\sqrt5+1}{\sqrt5-1}}=\sqrt{\frac{\sqrt5+1}{\sqrt5-1}\cdot\frac{\sqrt5+1}{\sqrt5+1}}=\sqrt{\frac{(\sqrt5+1)^2}{4}}=\frac{1+\sqrt5}2$$
For the expression to be evaluated, we have
\begin{align}
5x^2-5x-1&=5(x^2-x-\frac15)\\
&=5(x^2-x-\frac15-\frac45+\frac45)\\
&=5(x^2-x-1)+4
\end{align}
Since $x=\dfrac{1+\sqrt5}2$ is a root of $x^2-x-1=0$, we have the expression to be equal to $\boxed4$.
