Question

如何用matlab解以下方程：x=91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x

Answer 1

看看solve这个命令.在matlab命令行上敲入：

solve('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x')

我看了结果是跟那两位的一样,得到7个解,不过x=0显然不是解,估计是matlab的BUG.

因0不能作分母.一个笨方法是逐个带入求解,有matlab函数subs可以解决.

如下：

xx=solve('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x')

xx =

9.5928722289771455041249312194069

-51.25070353762559926595511337666

100.0

-1.7631487189817605177017457928844

-7.4742012011826256018294334313148

-0.34893975376738034980285890672882

0

subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(1))

ans =

1.4541648269870039213039013706974*10^(-37)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(2))

ans =

(-1.2652826131748627602783043114906)*10^(-36)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(3))

ans =

1.0285575569695015694726444700695*10^(-38)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(4))

ans =

(-5.8344113438106212736497260726423)*10^(-40)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(5))

ans =

3.2984175096138360958310753236859*10^(-36)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(6))

ans =

2.8887019080459322775106987459902*10^(-41)

>> subs('91.83/(2.07*(100-x)/x+1)+2.37/(0.359*(100-x)/x+1)+1.83/(0.084*(100-x)/x+1)+1.68/(0.0251*(100-x)/x+1)+1.32/(0.0075*(100-x)/x+1)+0.97/(0.00092*(100-x)/x+1)-x','x',xx(7))

? Error using ==> mupadfeval at 28

Error: Division by zero [_power];

during evaluation of 'mlsubs'

Error in ==> sym.subs at 219

G = sym(mupadfeval('mlsubs', charcmd(G), [x '=' charcmd(y)]));

最后带入0,出错了,因此是头6个解,看结果都已经到10的-30次方以下了,精度够了.