a*cos^2C/2+c*cos^2A/2=3b/2
a*cos^2(C/2)+c*cos^2(A/2)=3b/2
a(cosC+1)/2+c(cosA+1)/2=3b/2
a(cosC+1)+c(cosA+1)=3b
a*cosC+a+c*cosA+c=3b
acosC+c*cosA=3b-a-c
a*(a^2+b^2-c^2)/2ab+c*(c^2+b^2-a^2)/2bc=3b-a-c
(a^2+b^2-c^2)/2b+(c^2+b^2-a^2)/2b=3b-a-c
(a^2+b^2-c^2+c^2+b^2-a^2)/2b=3b-a-c
2b^2/2b=3b-a-c
b=3b-a-c
a+c=2