Question

Find the value of 27x³ + 8y³, if  3x + 2y = 20 and xy = \[\frac{14}{9}\]

Answer 1

Given  `3x+2y = 20,xy = 14/9`

On cubing both sides we get,

 `(3x+ 2y)^3 = (20)^3`

We shall use identity  `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`

`27x^3 + 8y^3 + 3(3x)(2y)(3x+2y) = 20 xx 20 xx 20`

     `27x^3 + 8y^3 + 18 (xy)(3x+ 2y)= 8000`

          `27x^3 + 8y^3 + 18 (14/9)(20) = 8000`

                                       ` 27x^3 + 8y^3 = 8000 - 560`

                                       `27x^3 + 8y^3 = 7440`

Hence the value of  ` 27x^3 + 8y^3 `is 7440 .