\(3x=7y\Rightarrow\frac{x}{7}=\frac{y}{3}\)
đặt \(k=\frac{x}{7}=\frac{y}{3}\Rightarrow x=7k,y=3k\)
\(\Rightarrow xy=7k.3k=21k^2=2100\Rightarrow k^2=100\Rightarrow\orbr{\begin{cases}k=10\\k=-10\end{cases}}\)
\(k=10\Rightarrow x=70,y=30\)
\(k=-10\Rightarrow x=-70,y=-30\)
Vậy x=70 và y=30, x=-70 và y=-30
\(3x=7y\)
\(\Leftrightarrow\frac{x}{7}=\frac{y}{3}\)
\(\Leftrightarrow\frac{x^2}{49}=\frac{xy}{21}=\frac{y^2}{9}\)
\(\Leftrightarrow\frac{x^2}{49}=\frac{y^2}{9}=\frac{2100}{21}=100\)
\(\Leftrightarrow\hept{\begin{cases}\frac{x^2}{49}=100\\\frac{y^2}{9}=100\end{cases}\Leftrightarrow\hept{\begin{cases}x^2=4900\\y^2=900\end{cases}}}\Leftrightarrow\hept{\begin{cases}x=\pm70\\y=\pm30\end{cases}}\)
Vậy \(\left(x,y\right)\in\left\{\left(-70,-30\right);\left(70,30\right)\right\}\)
!!!
\(3x=7y\Leftrightarrow\frac{x}{7}=\frac{y}{3}=k\left(k\ne0\right)\)
\(\Rightarrow x=7k;y=3k\)
\(xy=7k.3k=2100\Leftrightarrow21.k^2=2100\Leftrightarrow k^2=100\Leftrightarrow k=10\)hoặc \(k=-10\)
\(Th1\left(k=10\right)\)
\(\frac{x}{7}=10\Leftrightarrow x=70;\frac{y}{3}=10\Leftrightarrow y=30\)
\(Th2:\left(k=-10\right)\)
\(\frac{x}{7}=-10\Leftrightarrow x=-10;\frac{y}{3}=-10\Leftrightarrow y=-30\)
Vậy x = 70 và y = 30 hoặc x = -10 và y = -30
