在三角形ABC中,已知2B=A+C,b^2=ac,则B-A=?A.0 B.Π/6 C.Π/4

题目

在三角形ABC中,已知2B=A+C,b^2=ac,则B-A=?A.0 B.Π/6 C.Π/4
在三角形ABC中,已知2B=A+C,b^2=ac,则B-A=?
A.0 B.Π/6 C.Π/4 D.Π/3

答案

A + B + C = 180,2B = A + C => B = 60
b^2 = a^2 + c^2 - 2ac * cosB = a^2 + c^2 - ac = ac => (a - c)^2 = 0 => a = c => A = C = 60
B - A = 0