数学比较大小...求X^2+Y^2+1与2(X+Y-1)谁大谁小...

2019-03-29

优质解答

(x²+y²+1)-2(x+y-1)=(x²-2xy+1)+(y²-2y+1)+1=(x-1)²+(y-1)²+1平方大于等于0所以(x-1)²+(y-1)²+1≥1＞0所以(x²+y²+1)-2(x+y-1)＞0x²+y²+1＞2(x+y-1)... (x²+y²+1)-2(x+y-1)=(x²-2xy+1)+(y²-2y+1)+1=(x-1)²+(y-1)²+1平方大于等于0所以(x-1)²+(y-1)²+1≥1＞0所以(x²+y²+1)-2(x+y-1)＞0x²+y²+1＞2(x+y-1)...