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Question Number 187874 by mustafazaheen last updated on 23/Feb/23

h o w i s s o l u t i o n

{(\sqrt{2} - 1)}^{13} = x {(\sqrt{2} + 1)}^{221} = ?

1) x^{- 16} 2) x^{- 17} 3) x^{221} 4) x^{21}

Answered by som(math1967) last updated on 23/Feb/23

(\sqrt{2} + 1) (\sqrt{2} - 1) = 1

\Rightarrow (\sqrt{2} - 1) = \frac{1}{\sqrt{2} + 1}

{(\sqrt{2} - 1)}^{13} = x

\Rightarrow \frac{1}{{(\sqrt{2} + 1)}^{13}} = x

\Rightarrow {(\sqrt{2} + 1)}^{13} = \frac{1}{x}

\Rightarrow {{(\sqrt{2} + 1)}^{13}}^{17} = \frac{1}{x^{17}}

{(\sqrt{2} + 1)}^{221} = x^{- 17}

Answered by Sutrisno last updated on 23/Feb/23

{(\sqrt{2} + 1)}^{221} . \frac{{(\sqrt{2} - 1)}^{221}}{{(\sqrt{2} - 1)}^{221}}

= \frac{1}{{({(\sqrt{2} - 1)}^{13})}^{17}}

= \frac{1}{x^{17}}

= x^{- 17}

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