algebra

Plug x in:

\((\sqrt{2+\sqrt{2}})^4+\frac{4}{(\sqrt{2+\sqrt{2}})^4}\) 

Simplify:

\(6+4\sqrt2+\frac{4}{6+4\sqrt{2}}\)

The fraction's numerator and denominator can both be divided by 2:

\(6+4\sqrt2+\frac{2}{3+2\sqrt2}\)

I am not sure if this is the simplest form - someone please double check~!!!