2角B=角A+角C说明角B= 60° A+C=120°,由正弦定理：a/sinA = b/sinB = c/sinC = k ,sinB=(3)½/2,k=2/(3)½,a+c=k(sinA+sinC)=[2/（3）½]·(2sin(A+C)/2cos(A-C)/2) ,又0≤|A-C|＜120,故1＜a+c≤2