Question

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

\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]

Answer 1

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

Given \[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]

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

We can rearrange the  \[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]as

`= (5/x + 5x)[(5/x)^2 + (5x)^2 - (5/x)(5x)]`

` =(5/x)^3 + (5x)^3 `

` = (5/x) xx (5/x) xx (5/x) + (5x)xx (5x)xx(5x)`

` = 125/x^3 + 125x^3`

Now substituting the value x = 3 in `125/x^3 + 125x^3`

`= 125/x^3 + 125x^3`

`= 125/3^3 + 125 xx 3^3`

`= 125/27 + 125 xx 27`

`= 125/27 + 3375`

Taking Least common multiple, we get ​

` = 125 / 27 + (3375 xx 27)/(1xx 27)`

`= 125/27 + 91125/27`

` = (125 + 91125)/27`

` = 91250/27`

Hence the Product value of  \[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\] is ` = 91250/27`.