Question

If a + b = 10 and ab = 21, find the value of $a^3+b^3$.

Answer 1

a + b = 10, ab = 21

Cubing both sides,

$(a+b{)}^3=(10{)}^3\Rightarrow a^3+b^3+3ab(a+b)=1000\Rightarrow a^3+b^3+3\times 21\times 10=1000\Rightarrow a^3+b^3+630=1000\Rightarrow a^3+b^3=1000-630=370\therefore a^3+b^3=370$