Question

Tìm 2 số tự nhiên x,y biết tổng chúng gấp 2 lần tích chúng

Answer 1

Theo bài ta có: \(x+y=2xy\)

\(\Rightarrow x=2xy-y\)\(\Rightarrow x=y\left(2x-1\right)\)

\(\Rightarrow y=\frac{x}{2x-1}\left(2x-1\ne0\Rightarrow x\ne\frac{1}{2}\right)\)

\(\Rightarrow y=\frac{x}{2x-1}=\frac{2x-1+1}{2x-1}=\frac{2x-1}{2x-1}+\frac{1}{2x-1}=1+\frac{1}{2x-1}\in Z\)

\(\Rightarrow1⋮2x-1\Rightarrow2x-1\inƯ\left(1\right)=\left\{1;-1\right\}\)

\(\Rightarrow2x\in\left\{2;0\right\}\Rightarrow x\in\left\{1;0\right\}\)

*)Xét \(x=1\Rightarrow y=\frac{x}{2x-1}=\frac{1}{2\cdot1-1}=1\)

*)Xét \(x=0\Rightarrow y=\frac{x}{2x-1}=\frac{0}{2\cdot0-1}=0\)