Question

大家帮我看看这个方程用MATLAB怎么求解？

1819=20000*x*(1+x).^12/((1+x).^12-1)，请附上求解程序和答案，多谢。

Answer 1

复制下面两句就能解了
syms x;
x=solve(1819==20000*x*(1+x).^12/((1+x).^12-1))

结果是

x =

root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 1)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 2)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 3)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 4)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 5)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 6)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 7)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 8)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 9)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 10)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 11)
root(z^12 + (238181*z^11)/20000 + (324543*z^10)/5000 + (2139973*z^9)/10000 + (474991*z^8)/1000 + (2987919*z^7)/4000 + (2129919*z^6)/2500 + (3539811*z^5)/5000 + (1057419*z^4)/2500 + (699919*z^3)/4000 + (45991*z^2)/1000 + (59973*z)/10000 - 457/5000, z, 12)

追问

这个解是什么意思？能控制在四位有效数字以内吗？