一个三元代数不等式命题 设x,y,z;,n,m为正实数,当m>n.有:x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m) 当m=n时恒等成立,当m
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![一个三元代数不等式命题 设x,y,z;,n,m为正实数,当m>n.有:x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m) 当m=n时恒等成立,当m](/uploads/image/z/13868154-18-4.jpg?t=%E4%B8%80%E4%B8%AA%E4%B8%89%E5%85%83%E4%BB%A3%E6%95%B0%E4%B8%8D%E7%AD%89%E5%BC%8F%E5%91%BD%E9%A2%98+%E8%AE%BEx%2Cy%2Cz%3B%2Cn%2Cm%E4%B8%BA%E6%AD%A3%E5%AE%9E%E6%95%B0%2C%E5%BD%93m%3En.%E6%9C%89%3Ax%2F%5Bnx%2Bm%28y%2Bz%29%5D%2By%2F%5Bny%2Bm%28z%2Bx%29%5D%2Bz%2F%5Bnz%2Bm%28x%2By%29%5D%3E%3D3%2F%28n%2B2m%29+%E5%BD%93m%3Dn%E6%97%B6%E6%81%92%E7%AD%89%E6%88%90%E7%AB%8B%2C%E5%BD%93m)
一个三元代数不等式命题 设x,y,z;,n,m为正实数,当m>n.有:x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m) 当m=n时恒等成立,当m
一个三元代数不等式
命题 设x,y,z;,n,m为正实数,当m>n.有:
x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m)
当m=n时恒等成立,当m
一个三元代数不等式命题 设x,y,z;,n,m为正实数,当m>n.有:x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m) 当m=n时恒等成立,当m
命题 设x,y,z;,n,m为正实数,当m>n.有:
x/[nx+m(y+z)]+y/[ny+m(z+x)]+z/[nz+m(x+y)]>=3/(n+2m)
当m=n时恒等成立,当mn]
[m(b+c)-a(m+n)]/[a(n+2m)(m-n)]+[m(c+a)-b(m+n)]/[b(n+2m)(m-n)]+[m(a+b)-c(m+n)]/[c(n+2m)(m-n)]
= {m[(b+c)/a+(c+a)/b+(a+b)/c]-3(m+n)}/[(n+2m)(m-n)]
>=[6m-3(m+n)]/[(n+2m)(m-n)]=3/(n+2m)=右边.
当n>m时
左边=[m(b+c)-a(m+n)]/[a(n+2m)(m-n)]+[m(c+a)-b(m+n)]/[b(n+2m)(m-n)]+[m(a+b)-c(m+n)]/[c(n+2m)(m-n)]
={m[(b+c)/a+(c+a)/b+(a+b)/c]-3(m+n)}/[(n+2m)(m-n)]
={-m[(b+c)/a+(c+a)/b+(a+b)/c]+3(m+n)}/[(n+2m)(n-m)]
=