Question

find x3+y3 if x+y=3 and xy=2

Answer 1

We need to recall the following property of the cube of a sum.

$(a+b)^3=a^3+b^3+3ab(a+b)$

This problem is about the property of the cube of a sum.

Given:

$x+y=3$

$xy=2$

From the above property, we get

$x^3+y^3=(x+y)^3-3xy(x+y)$

$x^3+y^3=(3)^3-3(2)(3)$

$x^3+y^3=27-18$

$x^3+y^3=9$