△ABC中,内角A,B,C成等差数列,其对边a,b,c满足2b²=3bc,求A

△ABC中,内角A,B,C成等差数列,其对边a,b,c满足2b²=3bc,求A
△ABC中,内角A,B,C成等差数列,其对边a,b,c满足2b²=3bc,求A

△ABC中,内角A,B,C成等差数列,其对边a,b,c满足2b²=3bc,求A
A+B+C=3B=180 B=60
(a^2+c^2-b^2)/2ac=cosB=1/2 a^2+c^2-b^2=ac (1) 2b^2=3ac b^2=3ac/2(2) 代入(1)
得2a^2-5ac+2c^2=0 a=2c或a=c/2
当a=2c时,代入(2) b^2=3c^2 b=V3c b^2+c^2=3c^2+c^2=4c^2=a^2 A=90
当a=c/2时,代入(2) b^2=3c^2/2 b=V3c/2 a^2+b^2=c^2/4+3c^2/4=c^2 B=60 A=30