若x+y+z=xyz,求证x(1-y^2)(1-z^2)+y(1-x^2)(1-z^2)+z(1-x^2)(1-y^2)=4xyz

若xyz=1,求证 x^2/(y+z)+y^2/(z+x)+z^2/(x+y)≥3/2 已知x,y,z>0,xyz(x+y+z)=1,求证（x+y）(x+z)>=2 xyz=1,求证：x/(1+y)+y/(1+z)+z/(1+x) >=3/2 已知x^2+y^2+z^2=1,求证x+y+z-2xyz 若x,y,z∈R,且x+y+z=xyz,求证：(y+z)/x+(z+x)/y+(x+y)/z≥2(1/x+1/y+1/z)^2 若x,y,z∈R+,且x+y+z=xyz,求证:(y+z)/x+(z+x)/y+(x+y)/z＞2(1/x+1/y+1/z) 若x,y,z都是正实数,且x+y+z=xyz,求证:(y+z)/x+(z+x)/y+(x+y)/z≥2(1/x+1/y+1/z) 若x+y+z=xyz,求证x(1-y^2)(1-z^2)+y(1-x^2)(1-z^2)+z(1-x^2)(1-y^2)=4xyz 已知x,y,z都是正数,且xyz=1,求证：x^2/(y+z)+y^2/(x+z)+z^2/(x+y)≥3/2 已知x、y、z满足x+y+z=xyz,求证：x(1-y^2)(1-z^2)+y(1-x^2)(1-z^2)+z(1-x^2)(1-y^2)=4xyz xyz是正实数,求证：x/（y+z）+y/（z+x）+z/（x+y）>=3/2 x+y+z+2=xyz,x,y,z.为正实数,证明：xyz(x-1)(y-1)(z-1) 已知x+y+z=0,xyz=1,求证：x,y,z中必有一个大于2/3. x,y,z属于R,且xyz（x+y+z）=1,求证（x+y）（y+z）≥2 已知x+y+z=0求证x*x*x+y*y*y+z*z*z=3xyz 已知X,Y,Z为三个互不相等的数,且X+ 1/Y =Y+ 1/Z = Z+ 1/X.求证：(XYZ)^2 = 1 已知（x+y)(y+z)(z+x)=0,xyz不等于0 求证：1/x+1/y+1/z=1/(x+y+z) 已知x,y,z满足xyz=1,求证x^3/(x+y)+y^3/(y+z)+z^3/(z+x)大于等于3