Non-linear equation roots

If I have the equation: w = 2k / ln[(1+k)/(1-k)] ,w ∈ (0,1) knowing that k is a root how can I show that for fixed w , -k is also a root and that k is the only root in (0,1) ?

Answer 1

[Azzi Abdelmalek]

w=0.5
syms k
result=double(solve(w==2*k/log((1+k)/(1-k)),'k'))

[Monica]

Hi Azzi, I tried the method that you told me but it returns only one root : -0.957 which is not in the interval (0,1). Did I miss something?

Thanks a lot.

Answer 2

[Azzi Abdelmalek]

You can use fzero with starting interval

w=0.5;
f=@(k) 2*k/log((1+k)/(1-k))-w
x=fzero(f,[eps 1])