数学难题,求解-123400+36200/(1+r)^1+54800/(1+r)^2+48100/(1+r)^3 = 0望有心人解题,想知道如何算出 r ,麻烦每个步骤详解,有劳了.
2019-05-07
数学难题,求解
-123400+36200/(1+r)^1+54800/(1+r)^2+48100/(1+r)^3 = 0
望有心人解题,想知道如何算出 r ,麻烦每个步骤详解,有劳了.
优质解答
解方程-123400+36200/(1+r)+54800/(1+r)²+48100/(1+r)³= 0
化简系数得-1234+362/(1+r)+548/(1+r)²+481/(1+r)³= 0
两边同乘以(1+r)³得:
-1234(1+r)³+352(1+r)²+548(1+r)+481=0
设1+r=x,则有
-1234x³+352x²+548x+481=0
用逐步逼近法可得近似解x=1.0556
-1234×1.0556³+352×1.0556²+548×1.0556+481
=-1451.4875+392.2306+578.4688+481=0.212,
此时r=1.0556-1=0.0556.
解方程-123400+36200/(1+r)+54800/(1+r)²+48100/(1+r)³= 0
化简系数得-1234+362/(1+r)+548/(1+r)²+481/(1+r)³= 0
两边同乘以(1+r)³得:
-1234(1+r)³+352(1+r)²+548(1+r)+481=0
设1+r=x,则有
-1234x³+352x²+548x+481=0
用逐步逼近法可得近似解x=1.0556
-1234×1.0556³+352×1.0556²+548×1.0556+481
=-1451.4875+392.2306+578.4688+481=0.212,
此时r=1.0556-1=0.0556.