B=π/4,b=2,

a^2+c^2-b^2=2ac CosB
a^2+c^2-4=√2ac
a^2+c^2=√2ac+4
√2ac+4=a^2+c^2>=2ac

(2-√2)ac <=4
ac<=4/(2-√2)
ac<=4+2 √2

三角形ABC面积最大值
=1/2ac SinB
=1/2 (4+2 √2)√2/2
=√2+1