Question

If $p+q=12$ and $pq=22$, then find $p^2+q^2$.

Answer 1

Given:

$p+q=12$ and $pq=22$

Using,

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

$(p+q{)}^2=p^2+2pq+q^2$

$(12{)}^2=p^2+2(22)+q^2$

$144=p^2+q^2+44$

$p^2+q^2=144-44$

$\therefore p^2+q^2=100$

Hence, the required value is $100$.