∵a=2b+√2
ab+(c-1)²+1/4=0
∴（2b+√2)b+(c-1)²+1/4=0
∴(2b²+√2b+1/4)+(c-1)²=0
∴(√2b+1/2)²+(c-1)²=0
那么只有√2b+1/2=0且c-1=0
∴b=-√2/4,c=1,a=-√2/2+√2=√2/2
∴bc/a=-(√2/4)/(√2/2)=-1/2