已知x,y,z∈R+.求证(1+x2)(1+y2)(1+z2)≥8xyz

已知X,Y,Z∈R,且X+Y+Z=1,求证X2+Y2+Z2≥1/3 已知x,y,z∈R+.求证(1+x2)(1+y2)(1+z2)≥8xyz 已知x,y,z∈R,求证:x^2+y^2>=xy+x+y-1 设x,y,z∈R+,求证 2z2-x2-y2/(x+y)+2x2-y2-z2/(y+z)≥x2+z2-2y2/(x+z) 设x,y,z∈R+,求证 2z2-x2-y2/(x+y)+2x2-y2-z2/(y+z)≥x2+z2-2y2/(x+z) 已知x.y∈R,求证x2+y2+1≥x+y+xy 已知x,y∈R,求证x2-xy+y2>=x+y-1 已知x、y、z∈R＋,求证x⒋+y⒋+z⒋≥(x+y+z)xyz 高一 数学 数学 请详细解答,谢谢! (13 21:39:6)已知X,Y,Z∈R,且X+Y+Z=1,求证X2+Y2+Z2≥1/3 已知x,y,z∈R+,且x+y+z=8,xyz=5,求证：x,y,z中至少有一个小于1 已知x,y,z∈R,若x^4+y^4+z^4=1,求证x^2+y^2+z^2≤根号3 不等式的 已知x,y,z∈R,且x+y+z=1,求证√x+√y+√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 已知x,y∈R,求证（x2+y2）2≥xy(x+y)2 已知x,y∈R,且1≤x2+y2≤2,z=x2+xy+y2,则z的取值范围是 已知x+y+z=1,求证:x2+y2+z2≥1/3 已知xyz满足z+y+z=xyz 求证：x(1-y2)(1-z2)+y(1-x2)(1-z2)+z(1-x2)(1-y2)=4xyz 已知x.y.z属于R,求证:(1+x^2)(1+y^2)(1+z^2)大于等于8xyz