以知X+Y+Z=1求证（1+1/x)(1+1/Y)(1+1/z)>8

以知X+Y+Z=1求证（1+1/x)(1+1/Y)(1+1/z)>8 已知x,y,z>0,xyz(x+y+z)=1,求证（x+y）(x+z)>=2 x,y,z都>0.且x+y+z=1.求证1/x+4/x+9/z>=36 若xyz=1,求证 x^2/(y+z)+y^2/(z+x)+z^2/(x+y)≥3/2 xyz=1,求证：x/(1+y)+y/(1+z)+z/(1+x) >=3/2 x,y,z∈(0,1),且x+y+z=2,求证1 已知x^2+y^2+z^2=1,求证x+y+z-2xyz x+y+z=1,求证根号x+根号y+根号z 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) X,y,z>0且x+y+z=1,求证：（1/x-x)(1/y-y)(1/z-z)≥(8/3)^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,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)+y/(z+x)+z/(x+y)=1求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)=? 已知x,y,z∈R,求证:x^2+y^2>=xy+x+y-1 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∈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