Mathematics - Quadratic Equation Question with Solution | TestHub

Consider${\left(p^2+q^2\right)}^2-2p^2{q}^2=272$

${\left({\left(p+q\right)}^2-2pq\right)}^2-2p^2{q}^2=272$

$16-16pq+2p^2{q}^2=272$

${\left(pq\right)}^2-8pq-128=0$

${\left(pq\right)}^2-8pq-128=0$

$pq=\frac{8\pm 24}{2}=16,-8$

$\therefore pq=16$

$\therefore$Required equation

$: x^2-\left(2\right)x+16=0$