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