Question

If a/b + b/a = -1 (a,b≠0),the value of a^3 - b^3 is?​

Answer 1

Answer:

1. ${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} - xy ) \\ given \: \frac{a}{b} + \frac{b}{a} = - 1 \\ = \frac{ {a}^{2} + {b}^{2} }{ab} = - 1 \\ = {a}^{2} + {b}^{2} = - ab \: ..........eqn \: 1 \\ = {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + {b}^{2} + ab) \\ \: \: ......... eqn \: 2\\ we \: know \: that \: {a}^{2} + {b}^{2} = - ab \\ now \: sbstitute \: this \: in \: eqn \: 2 \\ we \: get \\ = (a - b)( - ab + ab) \\ = (a - b)(0) \\ = 0$

Step-by-step explanation:

see the above attachment