-Áp dụng BĐT AM-GM cho 2 số dương ta có:\(xy+1\ge2\sqrt{xy.1}=2\sqrt{xy}\)\(\Rightarrow y\ge xy+1\ge2\sqrt{xy}\)\(\Rightarrow\sqrt{y}\ge2\sqrt{x}\)\(\Rightarrow\sqrt{\dfrac{y}{x}}\ge2\)\(\Rightarrow\dfrac{y}{x}\ge4\)\(\Rightarrow\dfrac{x}{y}\le\dfrac{1}{4}\left(đpcm\right)\)-Dấu "=" xảy ra khi \(x=\dfrac{1}{2};y=2\) Câu trả lời: -Áp dụng BĐT AM-GM cho 2 số dương ta có:\(xy+1\ge2\sqrt{xy.1}=2\sqrt{xy}\)\(\Rightarrow y\ge xy+1\ge2\sqrt{xy}\)\(\Rightarrow\sqrt{y}\ge2\sqrt{x}\)\(\Rightarrow\sqrt{\dfrac{y}{x}}\ge2\)\(\Rightarrow\dfrac{y}{x}\ge4\)\(\Rightarrow\dfrac{x}{y}\le\dfrac{1}{4}\left(đpcm\right)\)-Dấu "=" xảy ra khi \(x=\dfrac{1}{2};y=2\)