已知 x+y+z=3 求证(x-1)^3+(y-1)^3+(z-1)^3-3(x-1)(y-1)(z-1)=0

已知x+y+z=0求证x*x*x+y*y*y+z*z*z=3xyz 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 已知x+1/y=y+1/z=z+1/x,求证y/x+z/y+x/z=3 , 已知x+1/y=y+1/z=z+1/x,求证y/x+z/y+x/z=3 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/x+y=y+z/2(y-z)=z+x/3(z-x),求证8x+9y+5z=0THX.. 已知x,y,z 大于0,x+y+z=2,求证 xz/y(y+z)+zy/x(x+y)+yx/z(z+x)大于等于2/3 已知X+Y+Z=0,求证X^3+Y^3+Z^3=3XYZ 已知：x+y+z=0,求证：x^3+y^3+z^3=3xyz 已知:x+y+z=0,求证x^3+y^3+z^3=3xyz 已知：x+y+z=0.求证：x三次+y上次+z三次=3xyz. 已知非负实数x,y,z满足x+y+z=3 (2),求证x^2/(1+x^4)+y^2/(1+y^4)+z^2/(1+z^4)≤1/(1+x)+1/(1+y)+1/(1+z) 一道高中不等式证明题已知正数x,y,z满足x+y+z=1求证：x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)>=1/3 已知正数x,y,z满足x+y+z=1求证x^2/y+2z +y^2/z+2x +z^2/x+2y≥1/3 已知x,y,z∈R+,且x+y+z=3,求证：x^2/（y^2+z^2+yz）+y^2/(x^2+z^2+zx）+z^2/(x^2+y^2+xy)≥1 已知2^x=3^y=6^z≠1,求证:1/x+1/y=1/z 已知2^x=3^y=6^z≠1,求证1/x十1/y=1/Z 已知2^x=3^y=6^z≠1,求证1/x+1/y=1/z