If $y =\sqrt{5+\sqrt{5-\sqrt{5+ \cdots}}}$, what is the value of $y^2-y$? If $$y =\sqrt{5+\sqrt{5-\sqrt{5 + \cdots}}},$$
what is the value of $y^2-y$ ?
I am unable to get the clue due to these alternative signs of plus and minus please help on this thanks...

Indeed, there is another way:
Let $x =\sqrt{5-\sqrt{5+\sqrt{5 - \cdots}}}$,
then it's easy to see 
$y^2 = 5 + x$, $x^2 = 5 - y$ 
then 
 $y^2 - x^2 = x+y$, therefore $y-x = 1$ 
Thus,
$$y^2 - y = y^2 - 1 - x = 5 + x - (1+x) =4$$
