一道“简单”的代数题

我自己没解出来,于是先后请教了几个不同专业、不同背景的人。期中包括econ、chemistry的graduate students,geology的Phd,geography的post-doc,sociology的graduate student和post-doc等,以及小熊!

最后由一个physics出身的biostats graduate student给出了一个合理解,在此特意感谢Jing Zhang同学!!

题目可以简化为:有三个未知实数p1,p2,p3,但已知 p1=q1^5000,p2=q2^4800,p3=q3^4900。其中q1、q2、q3已知,并且0<q1<1,0<q2<1,0<q3<1;"^"是指数符号,即p1等于q1的5000次方。求解p1/p、p2/p和p3/p,期中p=p1+p2+p3。

p1、p2、p3都是极小的数(小数点后百千位以上),一般的计算软件无法handle,基本上会将p1、p2、p3等同于0处理,导致p1/p、p2/p、p3/p无解(因为p约等于0)。

一个可行的解法如下:p1/p = 1/(p/p1)=1/((p1+p2+p3)/p1)=1/(1+p2/p1+p3/p1)=1/(1+exp(log(p2/p1))+exp(log(p3/p1)))

About Hongwei Xu

I'm a social demographer, a single-child, a husband, and a father.
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