灰常着急...若m²-n²=mn,求代数式m²/n²+n²/m²的值.

Question

灰常着急...
若m²-n²=mn,求代数式m²/n²+n²/m²的值.

Answer 1

m²-n²=mn
两边除以mn得
m/n-n/m=1
两边平方得
(m/n-n/m)²=1
m²/n²-2+n²/m²=1
∴m²/n²+n²/m²=3