Question Number 209304 by RoseAli last updated on 06/Jul/24
Answered by A5T last updated on 06/Jul/24
$${a}^{{x}} +{b}^{{x}} =\mathrm{62} \\ $$$${a}+{b}=\mathrm{8};{ab}=\mathrm{1} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\left({a}+{b}\right)^{\mathrm{2}} −\mathrm{2}{ab}=\mathrm{64}−\mathrm{2}=\mathrm{62} \\ $$$$\Rightarrow{x}=\mathrm{2} \\ $$
Commented by RoseAli last updated on 06/Jul/24
Thanks
Commented by Frix last updated on 06/Jul/24
$$\left(\mathrm{4}+\sqrt{\mathrm{15}}\right)^{−\mathrm{1}} =\mathrm{4}−\sqrt{\mathrm{15}}\:\Rightarrow\:{x}=\pm\mathrm{2} \\ $$