证：要证命题成立,只需证：x^2+y^2+z^2+1-x-y-z>0
即证：(x-1/2)^2+(y-1/2)^2+(z-1/2)^2+1/4>0
显然成立,
又因以上各步均可逆,所以愿不等式成立
(Sorry~开始题目抄错)已知x,y,z∈R,求证:x^2+y^2+z^2+1>x+y+z
2个回答
相关问题
-
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
-
已知x+y+z=1,x,y,z大于0,求证:x^2/(y+z)+y^2/(z+x)+z^2/(y+x)大于等于1/2
-
x,y,z∈R且x+y+z=1,x^2+y^2+z^2=1,x>y>z,求证:-1/3
-
已知x y z都属于R 2^x=3^y=6^z 求证 1/x+1/y=1/z
-
已知x,y,z是正实数.求证x^2/(y+x)+y^2/(x+z)+z^2/(x+y)≥x+y+z/2
-
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,z∈R+.求证(1+x2)(1+y2)(1+z2)≥8xyz
-
已知x,y,z成等差数列 求证:x2[y+z],y2[x+z],z2[x+y]成等差数列
-
已知x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求代数式x2/(y+z)+y2/(x+z)+z2/
-
已知x+y+z=1，求证x2+y2+z2≥13．