方程X y-8z=0.4x-2y-2z=0

实数x,y,z,满足那么x+y=6,z^2=xy-9,∴xy=z^+9,(x-y)^=(x+y)^-4xy=-4z^>=0,∴z=0,(x+y)^z=6^0=1.

1、(1)+(2)×4得11x-33z=0∴x=3z把x=3z代入(2)得6z+y-8z=0∴y=2z把x=3z,y=2z代入x²+y²-z²÷xy+yz得原式=(9z&

e^(-xy)-2z+e^z=0-ye^(-xy)-2z'(x)+e^zz'(x)=0z'(x)=ye^(-xy)/(e^z-2)-xe^(-xy)-2z'(y)+e^zz'(y)=0z'(y)=xe

e^y-e^x=xy两边求导,得e^y*y'-e^x=y+xy'(e^y-x)y'=(e^x+y)所以y'=(e^x+y)/(e^y-x)x=0时,e^y-e^0=0,则e^y=1,则y=0所以y'(

e^z-z+xy^3=0偏z/偏x：z'e^z-z'+y^3=0y^3=z'(1-e^z)z'=y^3/(1-e^z)偏z/偏y:z'e^z-z'+3xy^2=0z'=3xy^2/(1-e^z)偏z/

对方程e^(-xy)+2z-e^z=2两边微分,有：e^(-xy)*d(-xy)+2*dz-e^z*dz=0-e^(-xy)*(x*dy+y*dx)+2*dz-e^z*dz=0移项,得：(e^z-2)

由3x-4y-z=0得z=3x-4y③由2x+y-8z=0得y=8z-2x④④代入③得x=3z⑤y=2z将x,y代入(x^2+y^2+z^2)/(xy+yz+2zx)=(9z^2+4z^2+z^2)/

x^2+y^2+z^2-3xyz=0两边对x求偏导,2x+2z*dz/dx-3yz-3xydz/dx=0从中解得：dz/dx=(3yz-2x)/(2z-3xy)(1)同理：dz/dy=(3xz-2y)

令G(X,Y,Z)=F(xy,z-2x)GZ'=F'2GX'=yF'1-2F'2∂z/∂x=-GX'/GZ'=(2F'2-yF'1)/F'2Gy'=xF'1∂z/&

两端对x求偏导得：-ye^(-xy)-2(z/x)+(z/x)e^z=0,所以,z/x=ye^(-xy)/(e^z-2)两端对y求偏导得：-xe^(-xy)-2(z/y)+(z/y)e^z=0,所以,

x+2y-z=3e^(xy-xz)两边对x求导,z看成是x的函数求偏导得,y看成常数,得1-əz/əx=3(y-z-xəz/əx)e^(xy-xz)=><

(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)=(x+y)²+2z(x+y)+z²+(x-y)²-z²-2z(x+y)=(x+y)&

3x-4y＝z,2x+y＝8z,解得：x=3z,y=2zxy+yz分之x二次方+y二次方-z二次方=(x^2+y^2-z^2)/(xy+yz)=(9z^2+4z^2-z^2)/(6z^2+2z^2)=

对称性不妨设：x≥y≥za=|x-y|=x-y,b=|y-z|=y-z,c=|z-x|=x-z有：a、b、c≥0;c=a+b则：c≥a、b≥0A的最大值=c已知得出：16=a^2+b^2+c^2=2c

对,这个题就是采用隐函数求导Z对X的偏导数=-Fx/Fz,然后代入（1,2,0）解出Z对X的偏导数来做.如果结果不对应该是计算上出错了,原理就是隐函数求导.再问：我算来不对啊，书上直接对方程求X的偏导

由已知可得：z=-y/3,x=-7y/3,原式=（.=41/19

此题的意图在于x+y=?（用换元法）因此此题暗含需要在方程两式x+2y+3z=8；x+3y+5z=6中导出x+y有关的式子；因而涉及到要使用换元法,要在两式中导出x+y的新元；因此两式要乘公因式后相减

6x-8y-2z=06x+3y-24z=011y-22z=0y=2z3x-4(2z)-z=0x=3z(x²+y²-z²)/(xy+yz)=[(3z)^2+(2z)^2-z

2x+z=6,z-2y=8相减2x+z-z+2y=6-82x+2y=-2x+y=-1x^2+y^2+2xy=(x+y)^2=(-1)^2=1

2x+z=6,z-2y=8相减2x+z-z+2y=6-82x+2y=-2x+y=-1x^2+y^2+2xy=(x+y)^2=(-1)^2=1