已知a,b,c都是正实数,求证：1/2a+1/2b+1/2c>=1/(b+c)+1/(c+a)+1/(a+b)

证明：首先有1/a+1/b>=4/(a+b)（这个两边同分也可以简单得到证明）故1/a+1/b>=4/(a+b)1/a+1/c>=4/(a+c)1/c+1/b>=4/(c+b)=>2/a+2/b+2/c>=4/(a+b)+4/(b+c)+4/(a+c)=>1/(2a)+1/(2b)+1/(2c)>1/(a+b)+1/(a+c)+1/(b+c)当且仅当a=b=c等号成立证毕!