Question

Tìm x,y thuộc Z thoả

1/x+1/y = 1/2

Answer 1

\(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)

\(\Rightarrow\frac{1}{x}< \frac{1}{2}\)

\(\Rightarrow x>2\left(1\right)\) 

Giả sử x < y \(\Rightarrow\frac{1}{x}>\frac{1}{y}\)

\(\Rightarrow\frac{1}{x}+\frac{1}{x}>\frac{1}{x}+\frac{1}{y}\)

\(\Rightarrow\frac{2}{x}>\frac{1}{2}=\frac{2}{4}\)

\(\Rightarrow x< 4\left(2\right)\)

Từ (1) và (2) => 2 < x < 4

Mà \(x\in Z\Rightarrow x=3\)

\(\Rightarrow\frac{1}{y}=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}\Rightarrow y=6\)

Vậy \(\left[\begin{array}{nghiempt}x=3\\y=6\end{array}\right.\) hoặc \(\left[\begin{array}{nghiempt}x=6\\y=3\end{array}\right.\)