Question

If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a³ − b³ =

 

पर्याय

• 1

• -1

• \[\frac{1}{2}\]

• 0

Answer 1

Given  `a/b+b/a = -1`

Taking Least common multiple in  `a/b +b/a = -1 `we get,

` a/b + b/a  -1`

`(axx a)/(b xx a)+(bxxb)/(a xx b) = -1`

`a^2/(ab) + b^2/(ab) = -1`

`(a^2 + b^2)/(ab) = -1 `

             `a^2+b^2 = -1 xx ab`

             `a^2 +b^2 = -ab`

    `a^2 + b^2 + ab = 0`

Using identity  `a^3 - b^3= (a-b) (a^2 +ab +b^2)`

`a^3 -b^3 = (a-b)(a^2 + ab+b^2)`

`a^3 -b^3 = (a-b)(0)`

`a^3 - b^3 = 0`

Hence the value of `a^3 - b^2` is  0.