a=1,c=根号7,则解法如下：
∵4sin^2（A+B）/2）-cos2C=7/2
4sin^2[(180°-C)/2]-cos2C=7/2
4sin^2(90°-C/2)-cos2C=7/2
4cos^2(C/2)- cos2C=7/2
2(1+cosC)-(2cos^2C-1)=7/2
2+2cosC-2cos^2C+1=7/2
解得cosC＝1/2 ∴角C=60°
c^2=a^2+b^2-2ab*cosC
7=1+b^2-2b*1/2
b^2-b-6=0
(b-3)(b+2)=0
b=3,b=-2(舍)
S=1/2absinC=1/2*1*3*根号3/2=3/4 根号3.
∵a+b=5
∴(a+b)^2=a^2+b^2+2ab=25
∴a^2+b^2=25-2ab
根据余弦定理c^2=a^2+b^2-2abcosC
∴7=25-2ab-2ab*1/2
解得ab=6
则ΔABC面积＝1/2*sinc*ab=1/2*根号3/2*6=3倍根号3/2