Question

if a/b +b/a = -1 then find the value of a^3 -b^3

Answer 1

$given \: \: \frac{a}{b} + \frac{b}{a} = - 1 \\ \frac{ {a}^{2} + {b}^{2} }{ab} = - 1 \\ {a}^{2} + {b}^{2} = - ab \\ {a}^{2} + {b}^{2} + ab = 0 - - - (1) \\ \\ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ substituting \: \: from \: \: (1) \\ = (a - b) \times 0 = 0$

Answer 2

Given,a/b+b/a= -1

Solving it,

a^2/ab+b^2/ab= -1

=> a^2+b^2 = -ab

=> a^2+b^2+ab=0         .......................Eq.(1)

Now, a^3-b^3=(a-b)(a^2+ab+b^2)  ...................Eq.(2)

Substituiting the value of Eq.(1) into Eq.(2)

We get, a^3-b^3=(a-b)*0

Therefore, a^3-b^3=0.

Thanks!!!