已知实数mn满足m的平方减4m减一等于零,n的平方减4n减一等于0,n分之m加上m分之n等于多少.
人气:191 ℃ 时间:2019-12-12 13:16:07
解答
从m²-4m-1=0,n²-4n-1=0可知m和n分别为方程x²-4x-1=0的两个根所以m+n=4,mn=1
m/n+n/m
=(m²+n²)/mn
=(m²+2mn+n²-2mn)/mn
=[(m+n)²-2mn]/mn
=(4²-2)/1
=16-2
=14
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