Question

If
$9 {x}^{2} + 4 {y}^{2} = 72$
and xy = 6, Find the value of 3x + 2y.​

Answer 1

$\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}}{\color{pink}{:}}}}}$

$3x+4y=16$

$\implies (3x+4y)^2=16^2$

$\implies (3x+4y)(3x+4y)=256$

$\implies 9x^2+24xy+16y^2=256\text{.}$

Then $xy=4$

$\implies 9x^2+24(4)+16y^2=256$

$\implies 9x^2+96+16y^2=256$

$\implies 9x^2+16y^2=256-96$

$\implies 9x^2+16y^2=160$