整数x、y满足不等式x2+y2+1≤2x+2y,则x+y的值有(  ) A.1个 B.2个 C.3个 D.4个

问题描述:

整数x、y满足不等式x2+y2+1≤2x+2y,则x+y的值有(  )
A. 1个
B. 2个
C. 3个
D. 4个

x2+y2+1≤2x+2y变形为,x2-2x+1+y2-2y+1≤1,(x-1)2+(y-1)2≤1,而(x-1)2≥0,(y-1)2≥0,
可得以下几种情况:

x−1=0
y−1=0
x−1=±1
y−1=0
x−1=0
y−1=±1

故x+y的值有2,3,1三种情况
故应选:C.