a,b,c属于R+ 用排序不等式证明a^2/b+c+b^2/c+a+c^2/a+b>=1/2(a+b+c)注意是用排序不等式!2.用柯西不等式证明a^2011+b^2011+c^2011>=a^2010*b+b^2011*c+c^2011*a没有把题目弄反 ,原题就是这样
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![a,b,c属于R+ 用排序不等式证明a^2/b+c+b^2/c+a+c^2/a+b>=1/2(a+b+c)注意是用排序不等式!2.用柯西不等式证明a^2011+b^2011+c^2011>=a^2010*b+b^2011*c+c^2011*a没有把题目弄反 ,原题就是这样](/uploads/image/z/2725671-39-1.jpg?t=a%2Cb%2Cc%E5%B1%9E%E4%BA%8ER%2B+%E7%94%A8%E6%8E%92%E5%BA%8F%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%AF%81%E6%98%8Ea%5E2%2Fb%2Bc%2Bb%5E2%2Fc%2Ba%2Bc%5E2%2Fa%2Bb%3E%3D1%2F2%28a%2Bb%2Bc%29%E6%B3%A8%E6%84%8F%E6%98%AF%E7%94%A8%E6%8E%92%E5%BA%8F%E4%B8%8D%E7%AD%89%E5%BC%8F%212.%E7%94%A8%E6%9F%AF%E8%A5%BF%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%AF%81%E6%98%8Ea%5E2011%2Bb%5E2011%2Bc%5E2011%3E%3Da%5E2010%2Ab%2Bb%5E2011%2Ac%2Bc%5E2011%2Aa%E6%B2%A1%E6%9C%89%E6%8A%8A%E9%A2%98%E7%9B%AE%E5%BC%84%E5%8F%8D+%2C%E5%8E%9F%E9%A2%98%E5%B0%B1%E6%98%AF%E8%BF%99%E6%A0%B7)
a,b,c属于R+ 用排序不等式证明a^2/b+c+b^2/c+a+c^2/a+b>=1/2(a+b+c)注意是用排序不等式!2.用柯西不等式证明a^2011+b^2011+c^2011>=a^2010*b+b^2011*c+c^2011*a没有把题目弄反 ,原题就是这样
a,b,c属于R+ 用排序不等式证明a^2/b+c+b^2/c+a+c^2/a+b>=1/2(a+b+c)
注意是用排序不等式!
2.用柯西不等式证明a^2011+b^2011+c^2011>=a^2010*b+b^2011*c+c^2011*a
没有把题目弄反 ,原题就是这样
a,b,c属于R+ 用排序不等式证明a^2/b+c+b^2/c+a+c^2/a+b>=1/2(a+b+c)注意是用排序不等式!2.用柯西不等式证明a^2011+b^2011+c^2011>=a^2010*b+b^2011*c+c^2011*a没有把题目弄反 ,原题就是这样
a^2/(b+c)+b^2/(c+a)+c^2/(a+b)>=(a+b+c)/2.
证:1)a>=b>=c>0时a+b>=a+c>=b+c,a^2>=b^2>=c^2,
1/(b+c)>=1/(c+a)>=1/(a+b),
由排序不等式,a^2/(b+c)+b^2/(c+a)+c^2/(a+b)>=b^2/(b+c)+c^2/(c+a)+a^2/(a+b),①
a^2/(b+c)+b^2/(c+a)+c^2/(a+b)>=c^2/(b+c)+a^2/(c+a)+b^2/(a+b),②
b^2+c^2>=(1/2)(b+c)^2,余者类推,
[①+②]/2,a^2/(b+c)+b^2/(c+a)+c^2/(a+b)>=(1/2)[(b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)]
>=(1/2)[(b+c)/2+(c+a)/2+(a+b)/2]
=(1/2)(a+b+c),
2)0