a/sinA=b.sinB=c/sinC=2R
∴sinA=a/2R,sinB=b/2R,sinC=c/2R
∴2R(a²/4R-c²/4R²）=(√2a-b)b/2R
∴a²-c²=(√2a-b)b=√2ab-b²
∴a²+b²-c²=√2ab
余弦定理 cosC=(a²+b²-c²)/2ab=√2ab/2ab=√2/2
∴C=45°
S=0.5absinC=0.5*2RsinA*2RsinB*√2/2=√2R²*sinAsinB
2sinAsinB=-cos(A+B)+cos(A-B)=cosC+cos(A-B)=√2/2+cos(A-B)
所以A=B时sinAsinB有最大值(√2/2＋1)/2
S最大值为√2（√2/2＋1）R²/2
=（√2＋1）R²/2