Question

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]

Answer 1

In the given problem, we have to find the value of equation using identity

Given \[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]

We shall use the identity,`a^3 + b^3 = (a+b)(a^2 - ab + b^2)`

We can rearrange the \[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\] as

` = (x/7 + y/3)[(x/7)^2 + (y/3)^2 - (x/7)(y/3)]`

` = (x/7)^3 + (y/3)^3`

` = (x/7) xx (x/7) xx (x/7) + (y/3)xx (y/3)xx (y/3)`

` = x^3/343 + y^3/27`

Now substituting the value i`x =3,y = -1`n  `x^3/343 + y^3/27`

 ` = x^3/343 + y^3/27`

 `= 3^3/343 + (-1)^3/27`

` = 27/343 - 1/27`

Taking Least common multiple, we get 

` = (27 xx 27)/(343 xx 27) - (1 xx 343) / (27 xx 343)`

` = 729/9261 - 343/9261`

`= (729 - 343)/9261`

` = 386/9261`

Hence the Product value of  \[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]is ` = 386/9261`.