Ta có:
\(x^2.y^2=144\)
=> \(\left(xy\right)^2=144\)
=>\(\left[{}\begin{matrix}xy=12\\xy=-12\end{matrix}\right.\)
Lại có:
\(\dfrac{x}{3}=\dfrac{y}{4}\)
=> \(\dfrac{x}{3}.\dfrac{y}{4}=\dfrac{x}{3}.\dfrac{x}{3}=\dfrac{y}{4}.\dfrac{y}{4}\)
=> \(\dfrac{xy}{12}=\dfrac{x^2}{9}=\dfrac{y^2}{16}\)
+/ xy = 12
=> \(1=\dfrac{x^2}{9}=\dfrac{y^2}{16}\)
=> \(\left\{{}\begin{matrix}x^2=9\\y^2=16\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}x=\pm3\\y=\pm4\end{matrix}\right.\)
+/ xy = -12
=> \(-1=\dfrac{x^2}{9}=\dfrac{y^2}{16}\)
=> \(\left\{{}\begin{matrix}x^2=-9\\y^2=-16\end{matrix}\right.\)( vô lí - loại)
Vậy \(\left(x;y\right)\in\left\{\left(-3;-4\right);\left(3;4\right)\right\}\)
