已知正实数A B C满足1/A+2/B+3/C=1,求证A+B/2+C/3≥9
问题描述:
已知正实数A B C满足1/A+2/B+3/C=1,求证A+B/2+C/3≥9
答
A+B/2+C/3=(A+B/2+C/3)*1=(A+B/2+C/3)*(1/A+2/B+3/C)
>=(A*(1/A)+B/2*(2/B)+C/3*(3/C))^2=9
当且仅当A=3,B=6,C=9时等号成立