Question

 Giải :    \(\begin{cases}xy=-64\\\frac{1}{x}-\frac{1}{y}=\frac{1}{4}\end{cases}\)

Answer 1

\(\frac{1}{x}-\frac{1}{y}=\frac{1}{4}\Leftrightarrow\frac{y-x}{xy}=\frac{1}{4}\Leftrightarrow\frac{x-y}{64}=\frac{1}{4}\Leftrightarrow4\left(x-y\right)=64\Leftrightarrow x-y=16\)

\(\Rightarrow x=16+y\left(1\right)\)

Mà \(xy=-64\left(2\right)\)

Thay (1) vào (2) ta có \(\left(16+y\right)\cdot y=-64\Leftrightarrow16y+y^2=-64\Leftrightarrow y^2+16y+64=0\Leftrightarrow\left(y+8\right)^2=0\Leftrightarrow y+8=0\Leftrightarrow y=-8\)

Suy ra \(x=16+y=16-8=8\)