If-x-2-x-2-2-2-2-x-16-x-16-Any-help-

Question Number 138366 by KwesiDerek last updated on 12/Apr/21

If x^{2} + x^{- 2} = \sqrt{2 + \sqrt{2 + \sqrt{2}}}

x^{16} + x^{- 16} = ?

Any help

Answered by TheSupreme last updated on 14/Apr/21

x^{4} + 1 - \sqrt{2 + \sqrt{2 + \sqrt{2}}} x^{2} = 0

x^{2} = t a n d s o l v e f o r t

t h a n e v a l u a t e

t^{4} + \frac{1}{t^{4}}

Answered by Ñï= last updated on 14/Apr/21

x^{2} + x^{- 2} = \sqrt{{(x^{2} + x^{- 2})}^{2}} = \sqrt{2 + x^{4} + x^{- 4}}

= \sqrt{2 + \sqrt{{(x^{4} + x^{- 4})}^{2}}} = \sqrt{2 + \sqrt{2 + x^{8} + x^{- 8}}}

= \sqrt{2 + \sqrt{2 + \sqrt{{(x^{8} + x^{- 8})}^{2}}}} = \sqrt{2 + \sqrt{2 + \sqrt{2 + x^{16} + x^{- 16}}}}

\Rightarrow x^{16} + x^{- 16} = 0

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