a>b>c>1,p=2[(a+b)/2-(ab)^1/2〕,q=3[(a+b+c)/3-(abc)^1/3],比较pq的大小

a>b>c>1,p=2[(a+b)/2-(ab)^1/2〕,q=3[(a+b+c)/3-(abc)^1/3],比较pq的大小

p-q=3*(abc)^1/3-c-2*(ab)^1/2
=c[3*(ab/cc)^1/3-1-2*(ab/cc)1/2]
令（ab/cc）^1/6=t
p-q=c*[3t^2-1-2t^3]
=c*[3(tt-1)-2(ttt-1)]
=-c*(t-1)^2(2t+1)