证1/a+1/b+1/c≥2/(a+b)+2/(b+c)+2/(a+c)

问题描述:

证1/a+1/b+1/c≥2/(a+b)+2/(b+c)+2/(a+c)

1/a+1/b=a+b/ab≥4(a+b)/(a+b)^2=4/a+b同理.1/a+1/c=a+c/ac≥4(a+c)/(a+c)^2=4/a+c1/c+1/b=c+b/cb≥4(c+b)/(c+b)^2=4/c+b相加2(1/a+1/b+1/c)≥4/(a+b)+4/(b+c)+4/(a+c)所以1/a+1/b+1/c≥2/(a+b)+2/(b+c)+2/(a+c)...