Question

If a + b = 6 and ab = 8; find $a^3+b^3$

Answer 1

$a+b=6\Rightarrow (a+b{)}^3=(6{)}^3\Rightarrow a^3+b^3+3ab(a+b)=216\Rightarrow a^3+b^3+3\times 8\left(6\right)=216\Rightarrow a^3+b^3+144=216\Rightarrow a^3+b^3=216-144\Rightarrow a^3+b^3=72$.