Question

X-Y=7 and xy=20. find X^3-Y^3

Answer 1

Question:

If x - y = 7 and xy = 20 , then find the value of x^3 - y^3.

Given:

x - y = 7 ------(1)

xy = 20 ------(2)

To find:

x^3 - y^3 = ?

Solution:

We know that;

=> (x - y)^2 = x^2 + y^2 - 2•xy

=> (7)^2 = x^2 + y^2 - 2•20

{using eq-(1) and (2)}

=> 49 = x^2 + y^2 - 40

=> x^2 + y^2 = 49 + 40

=> x^2 + y^2 = 89 --------(3)

Also, we know that;

=> x^3 - y^3 = (x - y)(x^2 + y^2 + xy)

= 7(89 + 20)

{using eq-(1),(2) and (3)}

= 7•109

= 763

Hence,

The required value of x^3 - y^3 is 763.