已知2m²-5m-1=0,(1/n)²+5/n-2=0,且m不等于n,求代数式n/m+m/n的值

已知2m²-5m-1=0,(1/n)²+5/n-2=0,且m不等于n,求代数式n/m+m/n的值
已知2m²-5m-1=0,(1/n)²+5/n-2=0,且m不等于n,求代数式n/m+m/n的值

已知2m²-5m-1=0,(1/n)²+5/n-2=0,且m不等于n,求代数式n/m+m/n的值
(1/n)²+5/n-2=0
则2n²-5n-1=0
2m²-5m-1=0
所以m和n是方程的2x²-5x-1=0根
m+n=5/2,mn=-1/2
则m²+n²=(m+n)²-2mn=29/4
所以m/n=n/m=(m²+n²)/mn=-29/2