Maths Question

[匿名]

2010-04-11 2:12 am

Please help to find out the answer for X. Thanks!

1000 = 500/(1+X%) + 400/(1+X%)2 + 300/(1+X%)3 + 100/(1+X%)4
由於打不到次方的細數字 , 故上方的 2 , 3 & 4 分別為 ( 1+X% ) 的 2 次 , 3 次及 4次方

回答 (1)

用戶2053

2010-04-11 2:34 am

✔ 最佳答案

1000 = 500/(1+X%) + 400/(1+X%)2 + 300/(1+X%)3 + 100/(1+X%)4
Let 1/(1+X%) be y :
1000 = 500y + 400y^2 + 300y^3 + 100y^4
10 = 5y + 4y^2 + 3y^3 + y^4
y^4 + 3y^3 + 4y^2 + 5y - 10 = 0
用這個程式 :
http://www.easycalculation.com/algebra/quartic-equation.php
y1 = 0.8734475453055506
y2 = -2.7081866874222346
y3 = -0.582630428941658 + 1.9718141623627705 i
y4 = -0.582630428941658 - 1.9718141623627705 i
只考慮實根 :
y1 = 1/(1+X%) = 0.8734475453055506
X1 = 14.48884431
y2 = 1/(1+X%) = -2.7081866874222346
X2 = - 136.9250763

👍 0 👎 0