Question

3m方-6m分之m-3÷（m+2-m-2分之5）

Answer 1

解:∵m是方程x²+3x-1=0的根
∴m²+3m=1
∴(m-3)/(3m²-6m)÷[m+2-5/(m-2)]
=(m-3)/[3m(m-2)]÷[(m²-9)/(m-2)]
=(m-3)/[3m(m-2)]×[(m-2)/(m+3)(m-3)]
=1/[3m(m+3)]
=1/[3(m²+3m)]
=1/[3×1]
=1/3
本题不用解方程。否则两个根都需要代入，但是结果就一个。