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Question Number 167066 by mathlove last updated on 05/Mar/22

Commented by cortano1 last updated on 05/Mar/22

$$\mathrm{x}\sqrt{\mathrm{x}}=\mathrm{u}\Rightarrow \mathrm{x}={\mathrm{u}}^{\frac{2}{3}}$$$$\mathrm{f}\left(\mathrm{u}\right)=\frac{{\mathrm{u}}^{\frac{1}{3}}}{{\mathrm{u}}^{\frac{2}{3}}}=\frac{1}{\sqrt[3]{\mathrm{u}}}$$$$\mathrm{f}(-64)+\mathrm{f}(-8)+\mathrm{f}\left(1\right)+\mathrm{f}\left(27\right)=$$$$\frac{1}{-4}+\frac{1}{-2}+1+\frac{1}{3}=\frac{1}{2}-\frac{1}{4}+\frac{1}{3}$$$$=\frac{1}{4}+\frac{1}{3}=\frac{7}{12}$$

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