If $x+y=5$ and $xy=6$ then find $x^3+y^3$.

Given :

$x+y = 5$ and $xy = 6$.

To do :

We have to find the value of $x^3+y^3$.

Solution :

We know that,

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

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

$x^2+y^2=(5)^2-2(6)=25-12=13$

$x^3+y^3 = (x+y)(x^2+y^2 -xy) = (5)(13-6)$

         $= 5 \times 7= 35$

Therefore, the value of $x^3+y^3$ is 35.

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