ĐKXĐ: x<>0; y<>0
\(\frac{3}{y}-\frac{12}{xy}=1\)
=>\(\frac{3x-12}{xy}=1\)
=>3x-12=xy
\(\frac{x}{8}-\frac{1}{y}=\frac14\)
=>\(\frac{xy-8}{8y}=\frac{2y}{8y}\)
=>xy-8=2y
=>3x-12-8=2y
=>3x-20=2y
=>\(y=\frac{3x-20}{2}\)
3x-12=xy
=>\(x\cdot\frac{3x-20}{2}=3x-12\)
=>\(x\left(3x-20\right)=2\left(3x-12\right)\)
=>\(3x^2-20x-6x+24=0\)
=>\(3x^2-26x+24=0\)
=>\(\left[\begin{array}{l}x=\frac{13+\sqrt{97}}{3}\\ x=\frac{13-\sqrt{97}}{3}\end{array}\right.\) (nhận)
TH1: \(x=\frac{13+\sqrt{97}}{3}\)
=>\(y=\frac12\left(3x-20\right)=\frac12\left(3\cdot\frac{13+\sqrt{97}}{3}-20\right)=\frac12\left(13+\sqrt{97}-20\right)\)
\(=\frac12\left(\sqrt{97}-7\right)\) (nhận)
TH2: \(x=\frac{13-\sqrt{97}}{3}\)
=>\(y=\frac12\left(3x-20\right)=\frac12\left(3\cdot\frac{13-\sqrt{97}}{3}-20\right)=\frac12\left(13-\sqrt{97}-20\right)\)
\(=\frac12\left(-\sqrt{97}-7\right)\) (nhận)
