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Question-118002




Question Number 118002 by mmmmmm1 last updated on 14/Oct/20
Answered by TANMAY PANACEA last updated on 14/Oct/20
x^3 +(1/x^3 )+x+(1/x)  (x+(1/x))^3 −3(x+(1/x))+(x+(1/x))  now x+(1/x)=3+2(√2) +(1/(3+2(√2)))=3+2(√2) +3−2(√2) =6  required answer  6^3 −2×6  =216−12=204
$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+{x}+\frac{\mathrm{1}}{{x}} \\ $$$$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} −\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)+\left({x}+\frac{\mathrm{1}}{{x}}\right) \\ $$$${now}\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\:=\mathrm{6} \\ $$$${required}\:{answer} \\ $$$$\mathrm{6}^{\mathrm{3}} −\mathrm{2}×\mathrm{6} \\ $$$$=\mathrm{216}−\mathrm{12}=\mathrm{204} \\ $$

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