若|x-1| |Y-2|=0求 X Y的值

2x+y=(1/x+9/y)(2x+y)=2+(y/x)+(18x/y)+9=11+(y/x)+(18x/y)≥11+2√[(y/x)·(18x/y)]=11+2√18=11+6√2当且仅当y/x=1

2x-3y=0(1)3x-y-1=0(2)由（2）得y=3x-1(3)把y=3x-1代入(1)得2x-9x+3=0∴x=3/7把x=3/7代入（3）得y=2/7∴x=3/7y=2/7

Dx^y+x^-y=2根号2===>(x^y+x^-y)^2=8===>x^2y+x^-2y+2=8===>x^2y+x^-2y=6(x^y-x^-y)^2=x^2y+x^-2y-2=6-2=4==>

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

/>（x+y+3）(x-y-2)=0x,y互为相反数则x+y=0...(1)带入上式3（x-y-2）=0x-y=2...(2)联立（1）（2）得x=1,y=-1

原方程左边=（2x-y）（x+2y）=0所以x=y/2或x=-y/2将x的值分别代入到x+y/x-y得-3或-1/3

x=-t,t>0y=-2t/[t^2-t+1]=-2/[t+1/t-1]t+1/t>=2,y>=-2/(2-1)=-2x=-1时最小,为-2

因为X-Y=1所以原式=x*1+y*（-1）+2013=x-y+2013=1+2013=2014

2*x+8*y-x*y=02x+y8=xy>=2√2x*√8y=4√xy√xy>=4xy>=16x>=16/yx+y>=16/y+y>=2√16/y*√y=8所以最小值是8

(x*x+y*y)(x*x+y*y)-4x*x*y*y=(x^4-2x^2y^2+y^4)=(x^2-y^2)^2=0x^2=y^2x/y=±1(x*x+5xy+y*y)/(x*x+2xy+y*y)=

x^5+x^4y+x^4+x+y+1=0x^4(x+y+1)+x+y+1=0(x^4+1)(x+y+1)=0然后因为x^4+1不可能等于0所以只有x+y+1=0x+y+1=03x+2y=1这两个公式,

2x-y=0x-1=0x=1,y=2x-y=1-2=-1

x+y=1x-y=2(x+2y)(x-2y)-(2x-y)(-y-2x)=(x+2y)(x-2y)+(2x-y)(y+2x)=x²-4y²+4x²-y²=5x&

x^2+y^2-8x-10y+41=0x^2-8x+16+y^2-10y+25=0(x-4)^2+(y-5)^2=0所以x=4,y=5x/y+y/x＝4/5+5/4=0.8+1.25=2.05

这是很典型的一道均值不等式题,关键是乘以x+y因为x+y=1原式=(x+y)(8/x+2/y)=10+8y/x+2x/y>=10+8=18,所以最小值为18当x=2/3,y=1/3时取到最小值

x=1-2y∴x²+y²=4y²-4y+1+y²=5y²-4y+1=5（y-0.4）²+0.2所以最小值是0.2若x＞0,y＞0则1-2y＞

y'=3-2xy'/x=1=1y'/x=0=3

有题意得x+y-3>=0xy+x+y-2>=0因为根号x+y-3+绝对值xy+x+y-2=0则x+y-3=0xy+x+y-2=0xy=-1x+y=3x^2+y^2=11x/y+y/x=(x^2+y^2

2x-3y=02x=3yx=1.5y5x+4y/3x-2y=7.5y+4y/4.5y-2y=11.5y/2.5y=4.6

∵|x+2y-1|+y²+4y+4=0∴|x+2y-1|+(y+2)²=0∴x=5,y=-2(2x-y)²-2(2x-y)(x+2y)+(x+2y)²=[(2x