a: \(3x^2+2y^2=7xy\)
=>\(3x^2-7xy+2y^2=0\)
=>\(3x^2-6xy-xy+2y^2=0\)
=>\(3x\left(x-2y\right)-y\left(x-2y\right)=0\)
=>\(\left(x-2y\right)\left(3x-y\right)=0\)
=>\(\left[{}\begin{matrix}x-2y=0\\3x-y=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2y\\x=\dfrac{y}{3}\end{matrix}\right.\)
TH1: x=2y
\(P=\dfrac{3x+y}{-x+7y}\)
\(=\dfrac{3\cdot2y+y}{-2y+7y}=\dfrac{7y}{5y}=\dfrac{7}{5}\)
TH2: x=y/3
\(P=\dfrac{3x+y}{-x+7y}\)
\(=\dfrac{3\cdot\dfrac{y}{3}+y}{-\dfrac{y}{3}+7y}=\dfrac{2y}{\dfrac{20}{3}y}=2:\dfrac{20}{3}=2\cdot\dfrac{3}{20}=\dfrac{3}{10}\)
b: \(2x^2-7xy+x+3y^2-3y=0\)
=>\(\left(2x^2-7xy+3y^2\right)+\left(x-3y\right)=0\)
=>\(\left(2x^2-6xy-xy+3y^2\right)+\left(x-3y\right)=0\)
=>\(2x\left(x-3y\right)-y\left(x-3y\right)+\left(x-3y\right)=0\)
=>\(\left(x-3y\right)\left(2x-y+1\right)=0\)
mà 2x-y+1>0
nên x-3y=0
=>x=3y
\(M=\dfrac{3x-y}{x+3y}=\dfrac{3\cdot3y-y}{3y+3y}=\dfrac{8y}{6y}=\dfrac{4}{3}\)
