Question

x divided by Y + Y divided by X is equals to minus 1 then find x cube minus y cube

Answer 1

Dear student,


$$\begin{gathered} Giventhat:\frac{x}{y}+\frac{y}{x}=-1 \\ find:x³-y³ \\ solution \\ \frac{x}{y}+\frac{y}{x}=-1 \\ \frac{x²+y²}{xy}=-1 \\ \Rightarrow x²+y²=-xy \\ \Rightarrow x²+y²+xy=0 \\ \Rightarrow (x²+xy+y²)=0.......................\left(1\right) \\ Weknowthat,x³-y³=(x-y)(x²+xy+y²) \\ from\left(1\right), \\ (x²+xy+y²)=0 \\ x³-y³=(x-y)\times 0 \\ x³-y³=0.............ans \end{gathered}$$
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