利用正弦定理
a/sinA=b/sinB=c/sinC=2R
∵ asinA-csinC=asinB-bsinB
∴ a²-c²=ab-b²
∴ cosC=(a²+b²-c²)/(2ab)=ab/(2ab)=1/2
∴ C=60°
a/sinA=b/sinB=c/sinC=2R=2√2
a=2√2sinA,b=2√2sinB
S =absinC*(1/2)
=2√3sinAsinB
=√3[cos(A-B)-cos(A+B)]
=√3[cos(A-B)+1/2]
∴ A=B时,
S有最大值3√3/2