z=x三次方siny

z对x的偏导=cosx+cos(x+y)=0时,cosx=-cos(x+y)=cos(pi-x-y),所以x=pi-x-y.同理z对y的偏导=0时,有y=pi-x-y.所以x=y=pi/3.此时z=3

3次根号x=4,且根号y-2z+1+（2z-6）的平方=0x=64,y-2z+1=0,2z-6=0解得x=64,y=5,z=33次根号负x-y的3次方-z的3次方=-4-125-27=-156请采纳答

（x+1）的二次方+（y-1）+z的绝对值=0所以x+1=0,y-1=0,z=0所以x=-1,y=1,z=0所以A=-2-0=-2B=1-0+0=1C=1+2-0=3原式=A-2B+C-3A=-2A-

（x+1）^2+丨y-1丨+丨z丨=0因为（x+1）^2,丨y-1丨,丨z丨都是大于等于0的,而且最后结果为0,所以这三部分分别为0.也就是说x=-1,y=1,z=0之后你把X,Y,Z的值代入A,B,

(x+y+z)^3-x^3-y^3-z^3=(x+y+z)^3-x^3-(y^3+z^3)=(x+y+z-x)[(x+y+z)^2+x(x+y+z)+x^2]-(y+z)(y^2-yz+z^2)=(y

令x+y=a,x+z=b,x+w=c,则a+b+c=2x.@又x^3+y^3+z^3+w^3=(a-x)^3+(b-x)^3+(c-x)^3+x^3=0带入@则(a-b-c)^3+(b-a-c)^3+

(x+y)^3+(z-x)^3-(y+z)^3=[(x+y)^3-(y+z)^3]+(z-x)^3=[(x+y)-(y+z)][(x+y)^2+(x+y)(y+z)+(y+z)^2]+(z-x)^3=

X的三次方+Y的三次方+Z的三次方=（x+y）（x2-xy+y2）+Z的三次方=-z（x2-xy+y2）+Z的三次方（x+y=-z）=-z（x2-xy+y2-z2）=-z[x（x-y）+(y+z)(y

x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]/2≥0x^3+y^3+z^3≥3xyz

令2000x^3=2001y^3=2002z^3=N,题中方程立方得2000x^2+2001y^2+2000z^2=（3次√2000+3次√2001+3次√2002）^3两边同除以N左边：(2000x

x²y³z∧M＝x²y³z∧4∴M＝4

要使丨(三次根号X)-4丨+根号(Z-3)+(Y-2Z+1)二次方=0成立,须使得：三次根号X＝4且z-3=0且y－2z+1＝0解得x=64,z=3,y=5所以：三次根号(X+Y三次方+Z三次方)＝三

∂z/∂x=6x²y^4+12xy^3∂z/∂y=8x^3y^3+18x²y²那么再求二阶偏导数,得到∂

X+Y+Z=3,X^2+Y^2+Z^2=29X^3+Y^3+Z^3=45思路:轮称式,三元三次方程,代入法,过程比较复杂.答案为X=2,Y=4,Z=-3X=2,Y=-3,Z=4X=4,Y=2,Z=-3

1.为了简化算式,设A=2000的立方根,B=2001的立方根,C=2002的立方根A^3=2000,B^3=2001,C^3=2002A^3x^3=B^3y^3=C^z^3y=Ax/Bz=Ax/C2

/>x^3+y^3+z^3-3xyz=x^3+x^2y+x^2z+y^2x+y^3+y^2z+z^2x+z^2y+z^3-x^2y-y^2x-xyz-xyz-y^2z-yz^2-x^2z-xyz-z^

z=x^3+y^3+3xy∂z/∂x=3x^2+3y∂^2z/∂x^2=6x=A∂z/∂y=3y^2+3x∂^2z/

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设2000x3=2001y3=2002z3=k则2000x2=k/x2001y2=k/y2002z2=k/z2000的立方根=k的立方根/x2001的立方根=k的立方根/y2002的立方根=k的立方根

设A=三次根号K,则A=X·三次根号2007=Y·三次根号2008=Z·三次根号2009A／X＝三次根号2007,A／Y＝三次根号2008,A／Z＝三次根号2009.A／X＋A／Y＋A／Z＝三次根号2