Question

設x,y∈R⁺,且xy-(x+y)=1,則(    )

A.x+y≥(+1)                        B.xy≤+1

C.x+y≤(+1)²                            D.xy≥(+1)

Answer 1

解析:求xy的范圍,由條件xy-1=x+y≥,

即()²--1≥0.

∴(-1)²≥2.

結合xy=1+(x+y)＞1,

得≥+1.

∴xy≥(+1)².C,D錯誤.

再求x+y的范圍.

由條件有x+y+1=xy≤()²,

即(x+y)²-4(x+y)-4≥0.

∴(x+y-2)²≥8.結合x+y≥≥2(+1),得x+y≥2+2.

∴A選項正確.

答案:A