x>0,(xlnx)"=1/x>0,(alna+blnb+clnc)/(a+b+c)≥ln[(a^2+b^2+c^2)/(a+b+c)],a^a*b^b*c^c≥[(a^2+b^2+c^2)/(a+b+c)]^(a+b+c)≥[(a+b+c)/3]^(a+b+c)≥(abc)^[(a+b+c)/3] 当且仅当a=b=c时取等号.