Question Number 42118 by Akashuac last updated on 18/Aug/18
$$\mathrm{x}−\mathrm{4}=−\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{then}\:.\:\mathrm{prove}\:\mathrm{x}^{\mathrm{4}} −\mathrm{194}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} } \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 18/Aug/18
$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{4} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{4}^{\mathrm{2}} −\mathrm{2}=\mathrm{14} \\ $$$${x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }=\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} −\mathrm{2}=\mathrm{14}^{\mathrm{2}} −\mathrm{2}=\mathrm{194} \\ $$$${so}\:\:{x}^{\mathrm{4}} −\mathrm{194}=−\frac{\mathrm{1}}{{x}^{\mathrm{4}} } \\ $$$$ \\ $$
Commented by Akashuac last updated on 18/Aug/18
$$\mathrm{thanks} \\ $$