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