a,b,c为正实数,求证1/a+1/b+1/c>=1/根号ab+1/根号bc+1/根号ac
问题描述：
a,b,c为正实数,求证1/a+1/b+1/c>=1/根号ab+1/根号bc+1/根号ac
答
a,b,c为正实数,所以：
1/a+1/b>=2根号1/ab
1/a+1/c>=2根号1/ac
1/b+1/c>=2根号1/bc
以上三式相加得：
2(1/a+1/b+1/c)>=2[1/根号ab+1/根号bc+1/根号ac]
即：1/a+1/b+1/c>=1/根号ab+1/根号ac+1/根号bc