Question

△ABC的内角A,B,C的对边分别为a,b ,c,若a,b,c成等比数列,且a^2,b^2,c^2成等差数列,则cosB

Answer 1

a,b,c成等比数列 ====> b^2=ac

a^2,b^2,c^2成等差数列 ====> 2b^2=a^2+c^2

a^2+c^2=2b^2=2ac

(a-c)^2=0

a=c

a=b=c

B=60

cosB=1/2