平面z=x平方-2xy-y平方-8x 4y,求所有点,在该点的切线是水平的

/>x-3=y-2x-y=1y-2=z-1y-z=1x-z=2x²+y²+z²-xy-yz-zx=(1/2)(x²-2xy+y²+y²-2y

3x的平方乘y-[2x的平方乘y-(2xy的平方-x的平方乘z)-4x的平方乘z]-xyz,当x=2,y=3,z=1时,求值=3x²y-2x²y+2xy²-x²

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

答：x+y+z=3y=2zy≠0,则z≠0所以：y=2z/3x+2z/3+z=2zx=z/3令z=3k,y=2k,x=k(xy+yz+zx)/(x²+y²+z²)=(2k

应该是2x+5y-4=02x+5y=4原式=2^2x×2^56=2^(2x+5y)=2^4=16假设锐角是A和B则有sin²A+sin²B=1所以就是x1²+x2&sup

由x-3=y-2=z-1,得,x-y=1,y-z=1,x-z=2x的平方+y的平方+z的平方-xy-yz-zx=2（x2+y^2+z^2-xy-yz-zx）(1/2)=(2x2+2y^2+2z^2-2

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==>

就是求偏导Z’｜x=2x+y-3Z’｜y=x+2y-6令Z’｜x=0,Z’｜y=0,组合方程式得x=0,y=3即（0,3）就是Z的驻点,所以极值为f（x,y）=-9

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

处理这类比例问题,有一个通用方法如果：x:y:z=a:b:c可以设x=aky=bkz=ck带入计算,就行了自己来试试吧~

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-

已知x/3=y/1=z/2x=3yz=2yxy+yz+zx=993y^2+2y^2+6y^2=9911y^2=99y^2=92x^2+12y^2+9z^2=2*9y^2+12y^2+9*4y^2=66

2X-3y-z=0(1)x+3y-14z=0(2)(1)+(2)3x-15z=0x=5z代入(1)y=3z结果代入(x^2+3xY)÷(y^2+z^2)=(25z^2+3*5z*3z)÷(9z^2+z

由题意得｛x+y+z=02x-y-7z=0=｛x+z=-yβ2x-7z=ypβ+p得x=2z,把x=2z带入β=-3z当x=2z,β=-3z时原式=【3×2z×（-3z）-（4z）²】除以（

x^2-2xy+y^2-9z^2=(x-y)^2-(3z)^2=(x-y+3z)(x-y-3z)

解方程组：｛2x-3y-z=0.(1)｛x+3y-14z=0.(2)(1)+(2)得：3x-15z=0即：x=5z,代入（1）式得y=3z所以：(4x²-5xy+z²)/(xy+y

（x-y+z）(x-y-z)

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*

x²+y²+z²-xy-xz-yz=2（x²+y²+z²-xy-xz-yz）/2←合理配方=[（x-y）²+（y-z）²