Question

Tìm x, y thuộc Q sao cho: x -y = xy = x:y

Answer 1

Giải:

Ta có: \(x-y=xy\)

\(\Rightarrow x=xy+y\)

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

Mà \(x-y=x:y\)

\(\Rightarrow x+1=x:y\)

Ta có: \(x:y=x-y\)

\(\Rightarrow x+1=x-y\)

\(\Rightarrow y=-1\)

\(x-y=xy\)

\(\Rightarrow x-\left(-1\right)=x\left(-1\right)\)

\(\Rightarrow x+1=-x\)

\(\Rightarrow x+x=-1\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=\frac{-1}{2}\)

Vậy cặp số \(\left(x;y\right)\) là \(\left(-1;\frac{-1}{2}\right)\)

 

 

 

 

 

 

\(\Rightarrow y=-1\)

 

Answer 2

Ta có:

x - y = xy => x = xy + y = y.(x + 1) (1)

=> x : y = x + 1 = x - y (theo đề bài)

=> y = -1

Thay y = -1 vào (1) ta có: x = -1(x + 1) = -x - 1

=> x + x = -1 = 2x

=> \(x=\frac{-1}{2}\)

Vậy \(x=\frac{-1}{2};y=-1\)