f(x)=mn=√3sin(x/4)cos(x/4)+cos²(x/4)
=√3/2*sin(x/2)+1/2*[cos(x/2)+1]
=√3/2*sin(x/2)+1/2*cos(x/2)+1/2
=sin(x/2+30°)+1/2
∵acosC+1/2*c=b
∴2abcosC+bc=2b²
而a²+b²-c²=2abcosC
∴a²+b²-c²+bc=2b²
那么a²-b²-c²+bc=0,即b²+c²-a²=bc
∴cosA=(b²+c²-a²)/2bc=bc/2bc=1/2
∴A=60°
∴B+C=180°-A=120°
那么C=120°-B∈(0,90°)
∴30°