Question

若m²-n²=mn,求m²÷n²+n²÷m²的值。

Answer 1

∵m²-n²=mn①
①/m²得 1-n²/m²=n/m
∴n²/m²+n/m-1=0
同理m²/n²-m/n-1=0
将n/m和-m/n视为方程x²+x-1=0的两根
∵a=1,b=1,c=-1
∴m÷n-n÷m=-b/a=-1
(m÷n-n÷m)²=1
m²÷n²+n²÷m²-2=1
m²÷n²+n²÷m²=3

/为除号
望采纳 谢谢
之前看错提了 sorry

Answer 2

把已知条件等式两边平方整理得m^4+n^4=3(m^2)(n^2)
再将问题多项式通分整理可写成（m^4+n^4）/(m^2)(n^2)
将已知条件整理就可得到问题多项式值为3

Answer 3

m^2/n^2+n^2/m^2=[m^2-n^2)^2+2m^2n^2]/m^2n^2=3m^2n^2/m^2n^2=3