题目内容
比较x2+y2与2(x+y-1)的大小.
解：x2+y2-2(x+y-1)
=x2+y2-2x-2y+2
=x2-2x+1+y2-2y+1
=(x-1)2+(y-1)2≥0.
当x≠1或y≠1时，x2+y2-2(x+y-1)＞0,
即x2+y2＞2（x+y-1）;
当x=1且y=1时，x2+y2-2(x+y-1)=0,
即x2+y2=2(x+y-1).
故x2+y2≥2(x+y-1).
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题目内容
比较x2+y2与2(x+y-1)的大小.
解：x2+y2-2(x+y-1)
=x2+y2-2x-2y+2
=x2-2x+1+y2-2y+1
=(x-1)2+(y-1)2≥0.
当x≠1或y≠1时，x2+y2-2(x+y-1)＞0,
即x2+y2＞2（x+y-1）;
当x=1且y=1时，x2+y2-2(x+y-1)=0,
即x2+y2=2(x+y-1).
故x2+y2≥2(x+y-1).