cos(A+B-C)=1/4
cos(180°-C-C)=1/4
cos2C=-1/4
2cos^2C-1=-1/4
cos^2C=3/8
∵C是钝角
∴cosC=-√6/4
sinC=√(1-cos^2C)
=√(1-3/8)
=√10/4
sin(A+B)/sinA=2
sin(180°-C)/sinA=2
sinC/sinA=2
sinA=(√10/4)/2
=√10/8
cosA=√(1-sin^2A)
=√(1-10/64)
=3√6/8
sinB=sin(180°-(A+C))
=sin(A+C)
=sinAcosC+cosAsinC
=√10/8*(-√6/4)+3√6/8*(√10/4)
=-√15/16+3√15/16
=√15/8
b/sinB=a/sinA
b=a*sinB/sinA
=2*√15/8/(√10/8)
=√6