a^2=b(b+c),a^2=b^2+bc.cosA=(b^2+c^2-a^2)/(2bc)=(c-b)/(2b)........(1)cosB=(a^2+c^2-b^2)/(2ac)cos2B=[2(cosB)^2]-1=(c^2-b^2)/(2a^2)=(c-b)/(2b).......(2)所以有A=2B.
