Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{x-y}{2-5}=\dfrac{12}{-3}=-4\)
\(\Rightarrow\left\{{}\begin{matrix}x=-4.2=-8\\y=-4.5=-20\end{matrix}\right.\)
\(\dfrac{x}{2}=\dfrac{y}{3}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=2k\\y=3k\end{matrix}\right.\)
\(\Rightarrow6k^2=54\Rightarrow k^2=9\Rightarrow k=\pm3\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3.2=6\\y=3.3=9\end{matrix}\right.\\\left\{{}\begin{matrix}x=-3.2=-6\\y=-3.3=-9\end{matrix}\right.\end{matrix}\right.\)
c) \(3x=5y\Rightarrow\dfrac{x}{5}=\dfrac{y}{3}\Rightarrow\dfrac{x^2}{25}=\dfrac{y^2}{9}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x^2}{25}=\dfrac{y^2}{9}=\dfrac{x^2-y^2}{25-9}=\dfrac{1}{4}\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=\dfrac{1}{100}\Rightarrow x=\pm\dfrac{1}{10}\\y^2=\dfrac{1}{36}\Rightarrow y=\pm\dfrac{1}{6}\end{matrix}\right.\)
2)
\(\dfrac{a}{b}=\dfrac{c}{d}=k\)
\(\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)
\(\Rightarrow\dfrac{5a+3b}{5a-3b}=\dfrac{15bk+3b}{15bk-3b}=\dfrac{3b\left(5k+1\right)}{3b\left(5k-1\right)}=\dfrac{5k+1}{5k-1}\)
\(\Rightarrow\dfrac{5c+3d}{5c-3d}=\dfrac{15dk+3d}{15dk-3d}=\dfrac{3d\left(5k+1\right)}{3d\left(5k-1\right)}=\dfrac{5k+1}{5k-1}\)
\(\Rightarrow\dfrac{5a+3}{5a-3b}=\dfrac{5c+3d}{5c-3d}\rightarrowđpcm\)