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Calculate-the-sum-of-2-x-2-x-if-4-x-4-x-23-




Question Number 4413 by alib last updated on 22/Jan/16
Calculate the sum of 2^x +2^(−x) ,  if 4^x +4^(−x) =23
$$\boldsymbol{\mathrm{C}}\mathrm{alculate}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{2}^{\boldsymbol{{x}}} +\mathrm{2}^{−\boldsymbol{{x}}} , \\ $$$$\mathrm{if}\:\mathrm{4}^{\boldsymbol{{x}}} +\mathrm{4}^{−\boldsymbol{{x}}} =\mathrm{23} \\ $$$$ \\ $$
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
$$\left(\mathrm{2}^{{x}} +\mathrm{2}^{−{x}} \right)^{\mathrm{2}} =\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} +\mathrm{2}=\mathrm{25} \\ $$$$\mathrm{2}^{{x}} +\mathrm{2}^{−{x}} =\mathrm{5} \\ $$

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