∴√3(ccosA+acosC)=2bcosA，

∴√3b=2bcosA，

∴cosA=√3/2,A=π/6.

2.B=π/6=A，

∴b=a,C=2π/3，

According to the cosine theorem, the median line of BC is AM = √ [A2+(A/2) 2+A2/2] = (√ 7/2) A = √ 7,

∴a=2，

∴S△ABC=( 1/2)a^2*sinC=√3.