已知m^2-n^2=4mn,则代数式m^4+n^4/m^2n^2的值是多少

问题描述:

已知m^2-n^2=4mn,则代数式m^4+n^4/m^2n^2的值是多少

m²-n²=4mn
(m²-n²)²=(4mn)²
m^4-2m²n²+n^4=16m²n²
m^4+n^4=18m²n²
(m^4+n^4)/m²n²=18m²n²/m²n²=18

因为m²-n²=4mn
所以(m²-n²)²=(4mn)²
m^4-2m²n²+n^4=16m²n²
所以m^4+n^4=18m²n²
所以(m^4+n^4)/m²n²=18m²n²/m²n²=18