Question Number 197618 by srijanGuha last updated on 24/Sep/23
Answered by Rasheed.Sindhi last updated on 24/Sep/23
$$\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)=\mathrm{2} \\ $$$${x}+\frac{\mathrm{1}}{{x}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} =\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{3}} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{8}}{\mathrm{27}} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{3}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)=\frac{\mathrm{8}}{\mathrm{27}} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{2}=\frac{\mathrm{8}}{\mathrm{27}} \\ $$