Question

已知a，b满足方程a^2-2a-1=0，b^2-2b-1=0，求a/b+b/a的值

Answer 1

解由a，b满足方程a^2-2a-1=0，b^2-2b-1=0
则a，b是方程x^2-2x-1=0的根
即a+b=2，ab=-1
故a/b+b/a
=(a^2+b^2)/ab
=[(a+b)^2-2ab]/ab
=[2^2-2(-1)]/(-1)
=-6