A/b + b/a = - 1 then (a^ 3 -b^ 3 )=?

1.	A/b + b/a = - 1 then (a^ 3 -b^ 3 )=?
Answer» $\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{\dfrac{a}{<klux>B</klux>} + \dfrac{b}{a} = - 1} \end{cases}\end{gathered}\end{gathered}$ $\begin{gathered}\begin{gathered}\bf To \: Find - \begin{cases} &\sf{ {a}^{ 3} - {b}^{3} } \end{cases}\end{gathered}\end{gathered}$ $\large\underline\purple{\bold{Solution :- }}$ $\tt \longrightarrow \: Given \: \: \: \dfrac{a}{b} + \dfrac{b}{a} = - 1$ $\tt \longrightarrow \: \dfrac{ {a}^{2} + {b}^{2} }{ab} = - 1$ $\tt\implies \: {a}^{2} + {b}^{2} = - ab$ $\tt\implies \: {a}^{2} + {b}^{2} + ab = 0$ ☆ On MULTIPLY both SIDES by (a - b), we GET $\tt \longrightarrow \: (a - b)( {a}^{2} + ab + {b}^{2} ) = 0$ $\tt\implies \: {a}^{?} - {b}^{3} = 0$

Answer»

$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{\dfrac{a}{<klux>B</klux>} + \dfrac{b}{a} = - 1} \end{cases}\end{gathered}\end{gathered}$