Question

设x、y∈R⁺,且xy-(x+y)=1,则…(    )

A.x+y≥2(+1)                            B.xy≤+1

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

Answer 1

解析:求xy的范围,由条件xy-1=x+y≥2,

即()²-2-1≥0.

∴(-1)²≥2.

结合xy=1+(x+y)＞1,

得≥+1.

∴xy≥(+1)².C、D错误.

再求x+y的范围.

由条件有x+y+1=xy≤()²,

即(x+y)²-4(x+y)-4≥0.

∴(x+y-2)²≥8.结合x+y≥2≥2(+1),得x+y≥2+2.

∴A选项正确.

答案:A