Question

a/b + b/a = - 1 then (a^ 3 -b^ 3 )=?​

Answer 1

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{\dfrac{a}{b} + \dfrac{b}{a} = - 1} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find - \begin{cases} &\sf{ {a}^{ 3} - {b}^{3} }  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\tt \longrightarrow \: Given \: \: \: \dfrac{a}{b} + \dfrac{b}{a} = - 1$

$\tt \longrightarrow \: \dfrac{ {a}^{2} + {b}^{2} }{ab} = - 1$

$\tt\implies \: {a}^{2} + {b}^{2} = - ab$

$\tt\implies \: {a}^{2} + {b}^{2} + ab = 0$

☆ 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 2

Step-by-step explanation:

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