Question

If $a+b=7,ab=15,$ find $a^3+b^3$.

Answer 1

Since (a + b) = 7
Cubing both Sides, we get, $(a+b{)}^3=7^3$
$a^3+b^3+3ab(a+b)=343$
Substituting the value of (a + b) and ab, we get
$a^3+b^3+3\times 15\left(7\right)=343$
$\Rightarrow a^3+b^3+315=343$
$\Rightarrow a^3+b^3=343-315\Rightarrow a^3+b^3=28$