Question

If $3x+4y=18$ and $xy=6,$ find the value of $9x^2+16y^2.$

Answer 1

We have, $3x+4y=18$

on Squaring on both sides, we get

$\Rightarrow (3x+4y{)}^2=324$

$\Rightarrow (3x{)}^2+(4y{)}^2+24xy=324$

We have, $xy=6$

$\Rightarrow 9x^2+16y^2+24\times 6=324$

$\Rightarrow 9x^2+16y^2+144=324$

$\therefore 9x^2+16y^2=180$