SOS,比较大小,x×x+y×y+1与2(x+y-1),-

Question

SOS,
比较大小,x×x+y×y+1与2(x+y-1),-

Answer 1

x2+y2+1-2(x+y-1)=x2+y2+1-2x-2y+2=(x-1)2+(y-1)2+1
因为(x-1)2+(y-1)2>=0所以(x-1)2+(y-1)2+1>0
x,y后的2是平方.