求x^2 y^2-8x 10y 16=0

x^2+y^2-6x-8y+25=0x^2-6x+9+y^2-8y+16=0(x-3)^2+(y-4)^2=0∴x=3且y=4y/x-x/y=4/3-3/4=7/12

x^2+y^2-6x-8y+25=0[x-3]^2+[y-4]^2=0x-3=0===>x=3y-4=0===>y=4y/x-x/y=4/3-3/4=7/12

xy移项,两边再同除以xy,得,2/y+8/x=1,再用x+y乘以上面的再问：你确认？这样解不出来啊再问：你确认？这样解不出来啊再答：得，2x/y+8y/x+2+8再用基本不等式得，答案16再问：0.

如果你的上标是2次方的话可以这样做x+y-2=0可以推出x+y=2(X^-Y^)^-8(X^+Y^)=[(X+Y)(X-Y)]^-8(X^+Y^)=4(X-Y)^-8(X^+Y^)=4X^-8XY+4

x：y=8：3,设x=8t,y=3t,代入式子(2x+3y)/(x-2y)得,(2x+3y)/(x-2y)=（16t+9t）/(8t-6t)=12.5

根号(x+y-8)+根号(8-x-y)=根号(3x-y-4)+根号(x-2y+7),根据二次根式有意义得：X+Y-8≥0,8-X-Y≥0,∴X+Y≥8,X+Y≤8,∴X+Y=8,左边为0,右边两个非负

(x+y)/x=11/88x+8y=11y8x=3yy=8x/3(x-y)/(x+2y)=(x-8x/3)/(x+16x/3)=(-5x/3)/(19x/3)=-5/19

3x=8yx/y=8/3（1）x+y/y=x/y+1=8/3+1=11/3(2)2x+3y/x-2y分子分母同时除以y得=(2x/y+3)/(x/y-2)=(16/3+3)/(8/3-2)=(25/3

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=-3y=4式子等于-49/12

x+y=8,x-y=6求x^2-y^2-2x-2y的值x^2-y^2-2x-2y=(x+y)(x-y)-2(x+y)=8*6-2*8=32

X+Y分之X-Y等于3x=-2yX+Y分之2(x-y)减X+Y分之3X+Y=(-x-3y)/(x+y)=1

2x+2y=-8,.14x+y=15.21式*2-2式得3y=-21y=-7（x-y)^2-(3x+2y)^2=[（x-y)-(3x+2y)][（x-y)+(3x+2y)]=(-2x-3y)(4x+y

X=-3/4y=2

x^2+y^2-6x+8y+25=0x²-6x+9+y²+8y+16=0(x-3)²+(y+4)²=0x-3=0x=3y+4=0y=-4y^x=-4³

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

x^2+y^2-8x+10y+41=0(x-4)^2+(y+5)^2=0x=4,y=-5x+y=-1(x+y)^2013=-1

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+y/y=11/8说明11y=8（x+y）即8x=3y所以x-y/x+2y=3（x-y）/3(x+2y)=（3x-3y）/(3x+6y)=(3x-8x)/(3x+16x)=-5/19

(x²－4x＋4)＋(4y²＋8y＋4)=0(x－2)²＋4(y＋1)²=0则：x－2=0且y＋1=0得：x=2、y=－1x＋y=1