Question Number 195532 by bbbbbbbb last updated on 04/Aug/23
$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} −\mathrm{2}^{−\boldsymbol{\mathrm{x}}} =\mathrm{5}\:\boldsymbol{\mathrm{find}}\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} +\mathrm{4}^{−\boldsymbol{\mathrm{x}}} =? \\ $$$$\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{soon}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{rxame}}\:\boldsymbol{\mathrm{tomarrow}} \\ $$
Commented by bbbbbbbb last updated on 04/Aug/23
$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} −\mathrm{2}^{−\boldsymbol{\mathrm{x}}} =\mathrm{5}\:\boldsymbol{\mathrm{find}}\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} +\mathrm{4}^{−\boldsymbol{\mathrm{x}}} =? \\ $$$$\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{soon}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{rxame}}\:\boldsymbol{\mathrm{tomarrow}} \\ $$
Answered by AST last updated on 04/Aug/23
$$\mathrm{25}=\mathrm{5}^{\mathrm{2}} =\left(\mathrm{2}^{{x}} −\mathrm{2}^{−{x}} \right)^{\mathrm{2}} =\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} −\mathrm{2}\Rightarrow\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} =\mathrm{27} \\ $$