题目内容
试比较x2+y2与xy+x+y-1的大小．
∵x2+y2-（xy+x+y-1）
=x2-（y+1）x+y2-y+1
=(x-
)2-
(y+1)2+y2-y+1
=(x-
)2+
(y-1)2≥0（10分）
∴x2+y2≥xy+x+y-1
=x2-（y+1）x+y2-y+1
=(x-
| y+1 |
| 2 |
| 1 |
| 4 |
=(x-
| y+1 |
| 2 |
| 3 |
| 4 |
∴x2+y2≥xy+x+y-1
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