Question

If $3p+2q=7$ and $pq=3$, then find the value of $9p^2+4q^2$.

Answer 1

Given $3p+2q=7,pq=3$

$9p^2+4q^2=?$

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

$(3q{)}^2+(2q{)}^2=?$

$9p^2+4q^2=(3p+2q{)}^2-2(3p\left)\right(2q)$

$=(7{)}^2-12pq$

$=49-12\left(3\right)$

$=49-36$

$=13$

$\therefore 9p^2+4q^2=13$