x^4+y^4+1+8xyz-2(y^2z^2+z^2x^2+x^2y^2+x^2+y^2+z^2)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/07 02:58:14

x^4+y^4+z^4+1+8xyz-2(y^2z^2+z^2x^2+x^2y^2+x^2+y^2+z^2）
=（x^2+y^2)+(z^2+1)^2+8xyz-4x^2y^2-2x^2z^2-2y^2z^2-2x^2-2y^2-4z^2
=（x^2+y^2)+(z^2+1)^2+8xyz-2z^2(x^2+y^2)-2(x^2+y^2)-4x^2y^2-4z^2
=（x^2+y^2)+(z^2+1)^2-2(z^2+1)(x^2+y^2)+4(2xyz-x^2y^2-z^2)
=[(x^2+y^2)-(z^2+1)]^2-[2(xy-z)]^2
=(x^2+y^2-z^2-1+2xy-2z)(x^2+y^2-z^2-1-2xy+2z)

因式分解 (x+y+z)^2+yz(y+z)+xyz 已知 x,y,z都是正实数,且 x+y+z=xyz 证明 (y+x)/z+(y+z)/x+(z+x)/y≥2(1/x+1 已知4x-3y+z=0,x+2y-8z=0,xyz不等于0,求x+y-z/x-y+2z的值方程组X:Y:Z=4:7:8,X+Y+2Z=54 求XYZ x*x+y*y+2z*z-2x+4y+4z+7=0,求xyz的值 x^4+y^4+1+8xyz-2(y^2z^2+z^2x^2+x^2y^2+x^2+y^2+z^2) (y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z 因式分解：25x y^2 z^2 (x+y-z)-30xyz(z-x-y)^2+5x y z^3 (z-x-y) x,y,z正整数 x>y>z证明 x^2x +y^2y+z^2z>x^(y+z)*y^(x+z)*z^(x+y) 3道高数题,1,函数F(x,y,z)=(e^x) * y * (z^2) ,其中z=z(x,y)是由x+y+z+xyz= 方程组:x-2y+4z=0,2x+3y-3z=0...xyz不等于0,求(2x+y-z)\(2x-y+z) 已知方程组4x-y+3z=0 2x+y+6z=0且xyz不等于0,则x/y+y/z+z/x是多少