已知3x+4y+5z=1求证X^2+y^2+z^2大于等于1/50

已知x-y/x+y=y+z/2(y-z)=z+x/3(z-x),求证8x+9y+5z=0THX.. 已知3x+4y+5z=1求证X^2+y^2+z^2大于等于1/50 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 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∈R,若x^4+y^4+z^4=1,求证x^2+y^2+z^2≤根号3 已知x,y,z都是正数,且3^x=4^y=6^z 求证 1/z-1/x=1/2y 已知：x,y,z均是正实数,且3^x=4^y=6^z.求证：1/z-1/x=1/2y 已知x,y,z>0,xyz(x+y+z)=1,求证（x+y）(x+z)>=2 已知x+y+z=0求证x*x*x+y*y*y+z*z*z=3xyz 已知x:：y：z=3：4：5,(1)求x+y分之z的值；（2）若x+y+z=6,求x,y,z. 已知(x-z)^2-4(x-y)(y-z)=0,求证：2y=x+z 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=4:5:7,求:(1)2x+3y+z/5z; (2)x+y/y+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 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