Question

已知a和b为正数,A是a与b的等差中项,G是a与b的等比中项,且A=2G .求a/b的值

Answer 1

2A=a+b,G^2=ab,而A^2=4G^2

即(a+b)^2=16ab

令a/b=k>0,a=bk

b^2(k+1)^2=16b^2*k

(k+1)^2=16k

k^2-14k+1=0

k=7+4√3

k=7-4√3