2j:
\(\frac{2}{x}=\frac{3}{y}\) vsx.y=96
=> \(\frac{2}{x}=\frac{3}{y}\)-> \(\frac{x}{2}=\frac{y}{3}\)
Dat K =\(\frac{x}{2}=\frac{y}{3}\)
=> x=2.k;y=3.k
=>x.y=2.k.3.k=96
=>x.y=2.3.k2 =96
=>6.k2=96
=>k2=96:6
=>k2=16
=>k2=42
=>k=+-4
\(\Rightarrow\orbr{\orbr{\begin{cases}Q=-4\Rightarrow x=2.-4=-8;y=3.-4=-12\\Q=4\Rightarrow x=2.4=8;y=3.4=12\end{cases}}}\)
Vay (x;y)\(\in\left\{\left(-8;-12\right);\left(8;12\right)\right\}\)
x=8.
y=12.