1/ Đặt $\dfrac{x}{4}=\dfrac{y}{3}=k$
$\to \begin{cases}x=4k\\y=3k\end{cases}$
$\to xy=4k.3k=12k^2=12$
$\to k^2=1$
$\to k=\pm 1$
\(\to\left[ \begin{array}{l}x=4\\x=-4\end{array} \right.\)
\(\to\left[ \begin{array}{l}y=3\\y=-3\end{array} \right.\)
Vậy $(x,y)=\{(4;3);(-4;-4)\}$
2/ $2x=5y\to \dfrac{x}{5}=\dfrac{y}{2}$
Đặt $\dfrac{x}{5}=\dfrac{y}{2}=k$
$\to \begin{cases}x=5k\\y=2k\end{cases}$
$\to x^3+y^3=(5k)^3+(2k)^3=125k^3+8k^2=133k^3=133$
$\to k^3=1$
$\to k=1$
$\to \begin{cases}x=5\\y=2\end{cases}$
3/ $\dfrac{x}{4}=\dfrac{y}{7}=k$
$\to \begin{cases}x=4k\\y=7k\end{cases}$
$\to x^2-y^2=(4k)^2-(7y)^2=16k^2-49k^2=-33k^2=-33$
$\to k^2=1$
$\to k=\pm 1$
\(\to\left[ \begin{array}{l}x=4\\x=-4\end{array} \right.\)
\(\to\left[ \begin{array}{l}y=7\\y=-7\end{array} \right.\)
Vậy $(x;y)=\{(4;7);(-4;-7)\}$
