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If \(x = \sqrt{2 + \sqrt{2}} \) then what is \(x^4 + \frac{4}{x^4}\)

 Jul 18, 2020
 #1
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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~!!!

 Jul 18, 2020

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