已知x+y+z=1,求证x^2+y^2+z^2大于等于三分之一写出具体过程

已知x,y,z>0,xyz(x+y+z)=1,求证（x+y）(x+z)>=2 已知x,y,z∈R,求证:x^2+y^2>=xy+x+y-1 已知x^2+y^2+z^2=1,求证x+y+z-2xyz 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-z)^2-4(x-y)(y-z)=0,求证：2y=x+z 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 不等式证明 急 已知x,y,z 是正数.若 x/(x+2) +y/(y+2) +z/(z+2) =1求证 x^2/(x+2) +y^2/(y+2) +z^2/(z+2) >=1 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) 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 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 已知三个实数x,y,z满足条件(z-x)^2-4(x-y)(y-z)=0,求证:x,y,z成等差数列 已知实数x,y,z满足x+y+z=1,x^2+y^2+z^2=1/2求X,Y,Z∈{0,2/3},已知实数x,y,z满足x+y+z=1,x^2+y^2+z^2=1/2求证X,Y,Z∈{0,2/3}, 已知x、y、z是正实数,x+y+z=1 求证1/（1+x^2)+1/（1+y^2)+1/（1+z^2) 已知实数x,y,z满足x=6-y,z^2=xy-9,求证：x=y 已知X,Y,Z为正数,X+Y+Z=1,求证:X^2+Y^2+Z^2>=1/3 用柯西不等式的知识