x2+y2 xy+x+y-1x y属于R 比较大小 x2+y2 xy+x+y-1
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x2+y2xy+x+y-1xy属于R比较大小x2+y2xy+x+y-1x2+y2xy+x+y-1xy属于R比较大小x2+y2xy+x+y-1x2+y2xy+x+y-1xy属于R比较大小x2+y2xy+
x2+y2 xy+x+y-1x y属于R 比较大小 x2+y2 xy+x+y-1
x2+y2 xy+x+y-1
x y属于R 比较大小
x2+y2 xy+x+y-1
x2+y2 xy+x+y-1x y属于R 比较大小 x2+y2 xy+x+y-1
(x2+y2)-(xy+x+y-1)
=(1/2)*[(x^2-2xy+y^2)+(x^2-2x+1)+(y^2-2y+1)]
=(1/2)*[(x-y)^2+(x-1)^2+(y-1)^2]
因为(x-y)^2≥0,(x-1)^2≥0,(y-1)^2≥0
(三项都取=号,有解x=y=1)
所以
(x2+y2)-(xy+x+y-1)≥0
x^2+y^2≥xy+x+y-1
X
前面哪个大雨等于后面哪个
用前式减后式得
X^2+Y^2-XY-X-Y+1=1/2X^2+1/2X^2+1/2Y^2+1/2Y^2-XY-X-Y+1=
(1/2X^2-XY+1/2Y^2)+(1/2X^2-X+1/2)+(1/2Y^2-Y+1/2)=
(g2/2X-g2/2Y)^2+(g2/2X-g2/2)^2+(g2/2Y-g2/2)^2
当X=Y=1时上式等于0 其余上式大于0
所以前式大于等于后式
g2/2 是 2分子根号2的意思
x2+y2 xy+x+y-1x y属于R 比较大小 x2+y2 xy+x+y-1
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