Question

if a/b+b/a=-1 then a^3-b^3=
​

Answer 1

Answer:

The answer is 0

Step-by-step explanation:

hopefully this will help

Answer 2

$\huge\blue\star$$\bold\red{Question:-}$

$\mathrm{if\:a/b+b/a=(-1)\:then\:a³-b³=?}$

$\huge\blue\star$$\bold\red{Given:-}$

$\mathrm{if\:a/b+b/a=(-1)}$

$\huge\blue\star$$\bold\red{To\:find:-}$

$\mathrm{a³-b³=?}$

$\blue\star$$\bold\red{Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{a}{b} + \frac{b}{a} = ( - 1)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: ⇒ \frac{ {a}^{2} + {b}^{2} }{ab} = ( - 1)$

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

⠀⠀⠀⠀⠀⠀⠀-------$\fbox\green{equation\:1}$

$\mathrm{We\: know\:that,}$

a³ - b³ = (a - b) (a² + ab + b²)

= (a - b) ( a² + b² + ab)....$\fbox\green{equation\:2}$

$\mathrm{but\: from\:1st\:[a²+ b² = (-ab)]}$

:. $\mathrm{Substitute\:the\: value\:(a²-b²)\:in\:2}$

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

$\mathrm{but\:( - ab + ab)=0\:}$

$➟{a}^{3} - {b}^{3} = (a - b) \times 0$

$\huge\fbox\blue{a³-b³=0}$