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题目设a,b,c为正数且abc=1,求证1/a~3(b+c)+1/b~3(c+a)+1/c~3(a+b)≥3/2。(第36届IMO试题) 本题是一道非常难得的好题。它的九种证法,充分展现了对称不等式的内在魅力,值得探究。证法1 利用柯西不等式的推论:
The subject is set to a, b, c is positive and abc = 1, to verify 1/a~3(b+c)+1/b~3(c+a)+1/c~3(a+b)≥3 /2. (36th IMO question) This question is a very rare good question. Its nine authentication methods fully demonstrate the inherent charm of symmetric inequality and are worth exploring. Proof 1. Use the inference of Cauchy inequality: