How to find theta_k in terms of theta_i and theta_j in the following formula

 Theta_k *sqrt(1+theta_k^2) + arcsinh(theta_k) = {theta_j* sqrt(1+theta_j^2)+arcsinh(theta_j)}+{theta_i * sqrt(1+theta_i^2)+arcsinh(theta_i)}

Answer 1

[Walter Roberson]

 F = @(theta_k) (theta_k .* sqrt(1+theta_k.^2) + asinh(theta_k)) - ( (theta_j .* sqrt(1+theta_j.^2) + asinh(theta_j)) + (theta_i .* sqrt(1+theta_i.^2) + asinh(theta_i)));
 
 guess = rand();
 
 fsolve(F, guess)

[Hayam Wahdan]

thank you very much,

but when running these lines of code this error appear " Failure in initial objective function evaluation. FSOLVE cannot continue"

[Walter Roberson]

What are the initial values for theta_i and theta_j ?

Perhaps you did not define theta_i and theta_j before you defined F.

If you are trying to find a symbolic form for theta_k in terms of unresolved variables theta_i and theta_k then you are not going to be able to do that, at least not in a closed form.