解析：由正弦定理a/sinA=b/sinB=c/sinC=2R
∴a^2-c^2=(√3a-b)b=√3ab-b^2
即（a^2+b^2-c^2)/2ab=√3/2
∴cosC=√3/2
∠C=30°
∵a^2+b^2=√3ab+c^2
=√3ab+4R^2*(sin30°）^2
=√3ab+R^2≥2ab,
當(dāng)且僅當(dāng)a=b,取=
∴ab≤(2+√3)R^2
S△ABC=1/2*absinC=ab/4≤(2+√3)R^2/4
即S△ABC的最大值為(2+√3)R^2/4