Why I got complex answer while I know it should be real????

Hi

I have a function to be solved. while I know it has a real answer I got complex answer, I check with 2 of my friends, one got real answer and the other one get the complex one as mine. what should I do? by the way,I want to solve it symbolic, This is the function and answer:

commands:

syms('x')
F=0.21*(exp(-0.157-0.157*x))-x
 s=solve(F,x)
 X=subs(s)

answer:

F = 21/(100*exp((157*x)/1000 + 157/1000)) - x
 s =(1000*lambertw(0, -(100000*exp(157/1000))/3297))/157
 X = 15.0552 +15.0159i

the answer tha my friend got with the same commands:

F =(21*exp(- (157*x)/1000 - 157/1000))/100 - x
 s =(1000*lambertw(0, (3297*exp(-157/1000))/100000))/157
 X = 0.1746

Answer 1

[owr]

My guess, and this may be a long shot, is that somewhere along the way you took the sqrt of -1.

[Fatemeh Eslami]

thanks, but no, I dont. In fact, I have just write that one line command in my question.

Answer 2

[Shashank Prasanna]

I got the same as your friend. Try the following

syms x F s X real

[Shashank Prasanna]

It seems to me that your F is different from your friends.

[Fatemeh Eslami]

we both open the same mfile and run it in just separate computers.

[Fatemeh Eslami]

Thanks Benji Bowbow,

this works:) syms x F s X real just I want to know that if in other cases that I am not sure about the complexity or reality of the answers,using this method gives me the correct answer or not.

Answer 3

[Walter Roberson]

Both F are the same, but your solve() is returning the wrong answer. The lambertw argument is of the form A*exp(-B) but your solve() is instead forming 1/A * exp(B) .

Which MATLAB versions are the two of you running? Is one of you running with the Maple based symbolic toolbox, and the other running with the MuPAD based symbolic toolbox?

Note: complex values are not inherently wrong solutions. The general solution is not restricted to LambertW branch 0 the way the two solutions here show.