Question

If $2x÷3y=8$ and $xy=4$ then find the value of $4x^2+9y^2$

Answer 1

$\frac{2x}{3y}=8$ & $xy=4$

$\Rightarrow 2x=8\times 3yx.y=4$

$\Rightarrow x=4\times 3y12y.y=4$

$x=12y{y}^2=\frac{4}{12}\Rightarrow y=\sqrt{\frac{1}{3}}$

$x=\frac{12}{\sqrt{3}}9y^2=9\times \frac{1}{3}=3$

$4x^2=4\times \frac{{12}^2}{3}=192$

$\therefore 4x^2+9y^2=192+3=195$