设正实数a,b,c满足1/(a+b+1)+1/(b+c+1)+1/(c+a+1)≥1,证明:a+b+c≥ab+bc+ca

设正实数a,b,c满足1/(a+b+1)+1/(b+c+1)+1/(c+a+1)≥1,证明:a+b+c≥ab+bc+ca
设正实数a,b,c满足1/(a+b+1)+1/(b+c+1)+1/(c+a+1)≥1,证明:a+b+c≥ab+bc+ca

设正实数a,b,c满足1/(a+b+1)+1/(b+c+1)+1/(c+a+1)≥1,证明:a+b+c≥ab+bc+ca
设t为a,b,c中最小的数.
则
3/(2t+1) >= 1/(a+b+1)+1/(b+c+1)+1/(c+a+1) >=1
3/(2t+1) >= 1
解得1>=t
则a+b+c >=3t>=ab+bc+ca
证毕