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\(x\left(x-y\right)=\frac{3}{10};y\left(x-y\right)=-\frac{3}{50}\)
\(\Rightarrow\frac{x\left(x-y\right)}{y\left(x-y\right)}=\frac{\frac{3}{10}}{\frac{-3}{50}}\Rightarrow\frac{x}{y}=\frac{3}{10}.\frac{50}{-3}=-5\)
\(\Rightarrow x=-5y\)(1)
Thay (1) vào
\(x\left(x-y\right)=\frac{3}{10}\Rightarrow-5y\left(-5y-y\right)=\frac{3}{10}\)
\(\Rightarrow30y^2=\frac{3}{10}\Leftrightarrow y^2=\frac{3}{10}.\frac{1}{30}=\frac{1}{100}\Rightarrow y=\orbr{\begin{cases}\frac{1}{10}\\-\frac{1}{10}\end{cases}}\)
\(\Rightarrow x=\orbr{\begin{cases}\frac{1}{10}.-5=-\frac{1}{2}\\-\frac{1}{10}.-5=\frac{1}{2}\end{cases}}\)
x*(x-y)=3/10
y*(x-y)=-3/50
=>x*(x-y)-y*(x-y)=3/10-(-3/50)
=>(x-y)*(x-y)=15/50+3/50=18/50=9/25
=>x-y=(3/5;-3/5)
+)Nếu x-y=3/5=>x=1/2;y=-10
+)Nếu x-y=-3/5=>x=-1/2;y=10
\(\hept{\begin{cases}x\left(x-y\right)=\frac{3}{10}\\y\left(x-y\right)=-\frac{3}{50}\end{cases}}\Rightarrow\frac{x}{y}=-5\Rightarrow x=-5y\)
\(x\left(x-y\right)=-5y\left(-5y-y\right)=30y^2=\frac{3}{10}\Leftrightarrow\orbr{\begin{cases}y=\frac{1}{10}\Rightarrow x=-\frac{1}{2}\\y=-\frac{1}{10}\Rightarrow x=\frac{1}{2}\end{cases}}\)
\(x\left(x-y\right)-y\left(x-y\right)=\frac{3}{10}+\frac{3}{50}=\frac{18}{50}=\frac{9}{25}\)
\(\Rightarrow\left(x-y\right)\left(x-y\right)=\frac{9}{25}\)
\(\Rightarrow\left(x-y\right)^2=\orbr{\begin{cases}\left(\frac{3}{5}\right)^2\\\left(-\frac{3}{5}\right)^2\end{cases}}\)
\(\Rightarrow x-y=\orbr{\begin{cases}\frac{3}{5}\\-\frac{3}{5}\end{cases}}\)
\(\frac{x.\left(x-y\right)}{y.\left(x-y\right)}=\frac{3}{10}:-\frac{3}{50}=-5=\frac{x}{y}\)
\(x=-5y\Rightarrow-5y\left(-5y-y\right)=\frac{3}{10}\Rightarrow30y^2=\frac{3}{10}\Rightarrow y=\frac{1}{10}hoặcy=-\frac{1}{10}\)
với y=1/10 => x=-5.1/10=-1/2
với y= -1/10 => x= 1/2