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Question Number 174719 by AgniMath last updated on 09/Aug/22

Answered by behi834171 last updated on 09/Aug/22

$$\mathit{a}+\mathit{b}\ne 0$$$$\Rightarrow \frac{\mathit{a}+\mathit{b}}{\mathit{a}\mathit{b}}=\frac{1}{\mathit{a}+\mathit{b}}\Rightarrow {(\mathit{a}+\mathit{b})}^2=\mathit{a}\mathit{b}\Rightarrow$$$$\Rightarrow {\mathit{a}}^2+\mathit{a}\mathit{b}+{\mathit{b}}^2=0\stackrel{\mathit{a}\ne \mathit{b}}{\Rightarrow }(\mathit{a}-\mathit{b})({\mathit{a}}^2+\mathit{a}\mathit{b}+{\mathit{b}}^2)=0$$$$\Rightarrow {\mathit{a}}^3-{\mathit{b}}^3=0\Rightarrow {\mathit{a}}^3={\mathit{b}}^3.◼$$

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