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
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![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](/uploads/image/z/10198788-60-8.jpg?t=%E5%B7%B2%E7%9F%A52m%26%23178%3B-5m-1%3D0%2C%281%2Fn%29%26%23178%3B%2B5%2Fn-2%3D0%2C%E4%B8%94m%E4%B8%8D%E7%AD%89%E4%BA%8En%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8Fn%2Fm%2Bm%2Fn%E7%9A%84%E5%80%BC)
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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