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Question Number 4413 by alib last updated on 22/Jan/16

$$\mathbf{C}\mathrm{alculate}\mathrm{the}\mathrm{sum}\mathrm{of}{2}^{\mathit{x}}+2^{-\mathit{x}},$$$$\mathrm{if}{4}^{\mathit{x}}+4^{-\mathit{x}}=23$$$$$$

Answered by prakash jain last updated on 22/Jan/16

$${(2^x+2^{-x})}^2=4^x+4^{-x}+2=25$$$$2^x+2^{-x}=5$$

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