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# algebra

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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