Question

if a by b + B by a equal to -1 then a cube minus b cube equal to what​

Answer 1

GIVEN

$\frac{a}{b} + \frac{b}{a} = - 1\\ \\ \\ \implies \frac{ {a}^{2} + {b}^{2} }{ab} = - 1 \\ \\ \\ \implies {a}^{2} + {b}^{2} = - ab \: (eq.01)$

TO FIND :-

${a}^{3} - {b}^{3}$

SOLUTION :-

${a}^{3} - {b}^{3} \\ \\ \\ = (a - b)( {a}^{2} + {b}^{2} + ab) \: [IDENTITY] \\ \\ \\ = (a - b)( - ab + ab) \\ \\ \\ = ( a - b)(0) \\ \\ \\ = 0 \: (ans)$

Answer 2

Answer:

=0

Step-by-step explanation:

a/b+b/a=-1

a²+b²/ab=-1

a²+b²=-ab

or a²+b²+ab=0-------------(1)

Now a³-b³=(a-b)(a²+b²+ab)

=(a-b)*0

=0