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x-4-1-x-then-prove-x-4-194-1-x-4-




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

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