Question

If $a+b=4$ and $ab=-12$, then find $a^2-b^2$.

Answer 1

$(a-b{)}^2=a^2+b^2-2ab+2ab-2ab=(a+b{)}^2-4ab$

$\Rightarrow (a-b{)}^2=64$

$\Rightarrow a-b=\pm 8$

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

$=\pm \left(4\right)\left(8\right)=\pm 32$.