MathematicsIf ab+ba=-1, then the value of a3-b3 = ____.

If $\frac{a}{b} + \frac{b}{a} = - 1$ , then the value of $a^{3} - b^{3}$ = ____.

\frac{a}{b} + \frac{b}{a} = - 1

, then the value of

a^{3} - b^{3}

= 0.
Given,

\frac{a}{b} + \frac{b}{a} = - 1

.
Simplify the equation by taking the LCM of denominators.

\Rightarrow \frac{a^{2} + b^{2}}{ab} = - 1

\Rightarrow a^{2} + b^{2} = - ab

\Rightarrow a^{2} + b^{2} + ab = 0

We know that

a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + ab)

.
Substitute

a^{2} + b^{2} + ab = 0

\Rightarrow a^{3} - b^{3} = 0

Hence, the correct answer is 0.

JEE