Sorry for my last post it's my bad .So I ask to this (the true ^^)nested radical :
$$\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{\cdots }}}}}}}}=\frac{1+\sqrt{5}+\sqrt{30-6\sqrt{5}}}{4}$$
The period is $4$ and the related equation is :
$$\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2+x}}}}=x$$
There is a big similarity with this How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
Following the answer of Tito Piezas III can solve this nested radical (with $2$).
My question: Can someone explain these similarities between these two nested radicals ?
Any helps is highly appreciated .
Thanks a lot .