Question

If $a+b=9,$ and $ab=20$ find the value of $a^3+b^3$

Answer 1

We have ${(a+b)}^3=a^3+b^3+3ab(a+b)$

$\therefore a^3+b^3={(a+b)}^3-3ab(a+b)$

$={\left(9\right)}^3-3\times 20\left(9\right)$

$=729-540=189$

$\therefore a^3+b^3=189$