2√2(sin^2A-sin^2C)=(a-b)sinB
a/sinA=b/sinB=c/sinC=2R=2√2
原式可化为
(a^2-c^2)/(2√2)=(a-b)b/(2√2)
即a^2+b^2-c^2=ab
∴cosC=(a^2+b^2-c^2)/(2ab)=1/2
∴C=60°
∴c=2R*sinC=√6
∵a^2+b^2-c^2=ab,c=√6
∴a^2+b^2=c^2+ab=6+ab≥2ab
∴ab≤6
∴S△ABC=（1/2）*ab*sinC
=（√3/4）ab
≤3√3/2
即S△ABC最大值是3√3/2