Question

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

Options

• 1

   

• -1

• \[\frac{1}{2}\]

• 0

Answer 1

      Given  `a/b + b/a = 1`

`(a xx a)/(b xx a) +(b xx b) /(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)`we get,

`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^3 ` is 0 .