问题
解答题
试比较x2+y2与xy+x+y-1的大小．
答案
∵x2+y2-（xy+x+y-1）
=x2-（y+1）x+y2-y+1
=(x-
)2-y+1 2
(y+1)2+y2-y+11 4
=(x-
)2+y+1 2
(y-1)2≥0（10分）3 4
∴x2+y2≥xy+x+y-1
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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
(y+1)2+y2-y+11 4
=(x-
)2+y+1 2
(y-1)2≥0（10分）3 4
∴x2+y2≥xy+x+y-1