若m²-n²=mn,求m²÷n²+n²÷m²的值.

若m²-n²=mn,求m²÷n²+n²÷m²的值.
若m²-n²=mn,求m²÷n²+n²÷m²的值.

若m²-n²=mn,求m²÷n²+n²÷m²的值.
∵m²-n²=mn
∴(m²-n²)^2=(mn)^2
则 m^4+n^4-2m²n²=m²n²
从而 m^4+n^4=3m²n² ①
又 m²÷n²+n²÷m²=m^4/(m²n²)+n^4/(m²n²)=(m^4+n^4)/(m²n²) ②
由①②得 m²÷n²+n²÷m²=3m²n²/(m²n²)=3
∴m²÷n²+n²÷m²的值为3.