x平方-y平方 z平方 2xz
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2x²+2xy+y²-4x+z-2倍根号z-3+2=0可化为x²+2xy+y²+x²-4x+4+(z-3)-2倍根号(z-3)+1=0即(x+y)
/>因为:(x+y+z)^2=x^2+y^2+z^2+2xy+2xz+2yz由已知:x+y+z=2,xy+yz+xz=-5所以:2(xy+yz+xz)=-10带入,从而有:x^2+y^2+z^2=14
设x/2=y/3=z/4=a则:x=2a;y=3a;z=4a代入得:(xy+yz+zx)/(x^2+y^2+z^2)=(6a^2+12a^2+8a^2)/(4a^2+9a^2+16a^2)=26a^2
X+Y+Z=-2两边平方得:X²+Y²+Z²+2XY+2YZ+2XZ=4X²+Y²+Z²+2(XY+YZ+XZ)=4因为XY+YZ+XZ=1
X^2+Y^2+Z^2=XY+YZ+XZ则有2X^2+2Y^2+2Z^2-2XY-2YZ-2XZ=0==>(X-Y)^2+(Y-Z)^2+(Z-X)^2=0必然X-Y=0,Y-Z=0,Z-X=0==>
设x/2=y/3=z/4=a,则x=2a,y=3a,z=4axy+yz+xz=2a*3a+3a*4a+4a*2a=26a*axx+yy+zz=2a*2a+3a*3a+4a*4a=29a*a则结果为26
根据题目可知:Y=2X;Z=3X则:原式=(X^2+4X^2+9X^2)/(2X^2-12X^2+9X^2)=-14
|2x-3y-8z|+|x+y+z|=0说明:2x-3y-8z=0且x+y+z=0,由此可得到;x=z,y=-2z;(xz^2+yz^2)(x^2-y)/x=z^2(x+y)(z^2+2z)/z=-z
X^2+Y^2+Z^2=(X+Y+Z)^2-2(XY+YZ+ZX)=2^2-2X1=4-2=2
设a=x-y,b=y-z,-a-b=z-x(y-z)平方+(x-y)平方+(z-x)平方=(y+z-2x)平方+(z+x-2y)平方+(x+y-2z)平方b^2+a^2+(-a-b)^2=(-a-b-
原式=(x+y)(x-y)+z(x-y)=(x-y)(x+y+z)=0
(X+Y+Z)的平方就是4,展开就是X的平方+Y的平方+Z的平方+2XY+2XZ+2YZ=4.XY+YZ+XZ=5.则2XY+2YZ+2XZ=10.故答案就是-6
x+y+z=-2,xy+yz+xz=1x的平方+y的平方+z的平方=(x+y+z)^2-2(xy+yz+xz)=4-2=2
首先du/dx=z+x*dz/dx而Z=Z(x,y)由方程x²z+2y²z²+y=0确定,对x求导得到2xz+x²*dz/dx+2y²*2z*dz/d
2x的平方+3xy-9y的平方+z的平方+3xz=(2x-3y)(x+3y)+3xz+z²=(2x-3y+z)(x+3y+z)=02x-3yzx+3yz
x:y:z=1:2:3y=2x,z=3xxy+yz+zx=2x^2+6x^2+3x^2=11x^2=66x^2=6y^2=4x^2=24z^2=9x^2=542x的平方+12y的平方-9z的平方=2*
∵3y=x+2z∴x+2z-3y=0x平方-9y平方+4z平方+4xz=x^2-9y^2+4z^+4xz=(x+2z)^2-(3y)^2=(x+2z-3y)(x+2z+3y)=0*(x+2z+3y)=
-3y=x+2z(1)(1)式两边同时平方,即::(-3y)^2=(x+2z)^29y^2=x^2+4xz+4z^2x^2-9y^2+4z^2+4xz=-9y^2+(x^2+4z^2+4xz)=-9y
x²+y²+z²-xy-xz-yz=2(x²+y²+z²-xy-xz-yz)/2←合理配方=[(x-y)²+(y-z)²