If $a + b = 6$ and $a^{2} + b^{2} = 20$, find the value of $a^{3} + b^{3}$.

Question

Aicharya · Accepted Answer

First $ab = \dfrac{(a+b)^{2} - (a^{2}+b^{2})}{2} = \dfrac{36-20}{2} = 8$. Then $a^{3}+b^{3} = (a+b)(a^{2} - ab + b^{2}) = 6(20 - 8) = 72$.

Solution