Question

If (a)/(b)+(b)/(a)=-1(a b!=0) the value of a^(3)-b^(3) is:
a) 1
b) -1
c) 0
d) 1/2​

Answer 1

$\star\:\:\bf\large\underline\blue{Question:-}$

• If $\frac{a}{b} + \frac{b}{a} = - 1$ and $a \neq b$ find the value of ${a}^{3} - {b}^{3}$

$\star\:\:\bf\large\underline\blue{Solution}$

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

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

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

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

Now,

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

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

$= (a - b) \times 0$

$= 0$

$\star\:\:\bf\large\underline\blue{Answer:-}$

• ${a}^{3} - {b}^{3} = 0$