Mathematics - Quadratic Equation Question with Solution | TestHub

Given,

$p^4+q^4=369\Rightarrow {\left(p^2+q^2\right)}^2-2{\left(pq\right)}^2=369$

$\Rightarrow {\left({\left(p+q\right)}^2-2pq\right)}^2-2{\left(pq\right)}^2=369$

$\Rightarrow {\left(9-2pq\right)}^2-2{\left(pq\right)}^2=369$

$\Rightarrow {\left(pq\right)}^2-18\left(pq\right)-144=0$  $\Rightarrow pq=24\left(\text{rejected}\right),-6$

Now, ${\left(\frac{1}{p}+\frac{1}{q}\right)}^{-2}=\frac{{\left(pq\right)}^2}{{\left(p+q\right)}^2}=\frac{{\left(pq\right)}^2}{9}=4$