Question Number 43226 by veerendravyas1974@gmail.com last updated on 08/Sep/18
$$ \\ $$$${If}\left({x}−\frac{\mathrm{1}}{{x}}=\mathrm{7}\right){thenthevalueofx}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }{is}? \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 08/Sep/18
$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\left({x}−\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} +\mathrm{2}.{x}.\frac{\mathrm{1}}{{x}}=\mathrm{51} \\ $$$${x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }=\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} −\mathrm{2}.{x}^{\mathrm{2}} .\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$$\:\:=\left(\mathrm{51}\right)^{\mathrm{2}} −\mathrm{2} \\ $$$$=\mathrm{2601}−\mathrm{2} \\ $$$$=\mathrm{2599} \\ $$