根据正弦定理
a/sinA=b/sinB=c/sinC=2R,得
sinA=a/(2R)
sinB=b/(2R)
sinC=c/(2R)
代入2R（sin^2A-sin^2C)＝（√2a-b)*sinB,得
a^2+b^2-c^2=ab√2
而a^2+b^2-c^2=2abcosC,所以
2abcosC=ab√2,得
cosC=√2/2
C=45°
S=1/2*absinC
=√2R^2sinAsinB
=√2R^2/2[cos(A-B)-cos(A+B)]
=√2R^2/2[cos(A-B)-cos135°]
=√2R^2/2[cos(A-B)+√2/2]
≤√2R^2/2（1+√2/2）
=（1+√2)*R^2/2
当且仅当A=B时,S最大为：（1+√2)*R^2/2