已知△abc中角abc的对边分别为abc,满足a^2-c^2=2b

问题描述:

已知△abc中角abc的对边分别为abc,满足a^2-c^2=2b
(1)若△abc的面积为2,求c(sinA+cosA)的最小值;
(2)若sinAcosC=3cosAsinC,求b

a²-c²=2b
a²=b²+c²-2bccosA
b²-2bccosA-2b=0
sinAcosC=3cosAsinC
sinAcosC+cosAsinC=4cosAsinC
sin(A+C)=4cosAsinC
sinB=4cosAsinC
cosA=sinB/4sinC=b/4c
b²-2bc(b/4c)-2b=0
b²/2 -2b=0
b=4