题目

证明：x2+y2+1>2(x-y-1)

提问时间：2020-06-25

答案

x2+y2+1-2(x-y-1) =x2+y2+1-2x+2y+2 =x2+y2-2x+2y+1+1+1 =(x-1)2+(y+1)2+1 (x-1)2+(y+1)2>=0 (x-1)2+(y+1)2+1>=1>0 x2+y2+1-2(x-y-1) >0 x2+y2+1>2(x-y-1)