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Question-209304




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

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