Question

If $a+b=10$ and $ab=2$, then find the value of $a^3+b^3$.

Answer 1

$a^3+b^3=(a+b)(a^2+b^2-ab)$

$=\left(10\right)\left(\right(a+b{)}^2-2ab-ab)$

$=\left(10\right)\left(\right(10{)}^2-3\left(2\right))$

$=10(100-6)$

$=10\left(94\right)$

$=940$