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

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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)}

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Accepted Answer

Walter Roberson
Walter Roberson on 21 Dec 2019
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)

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Hayam Wahdan
Hayam Wahdan on 22 Dec 2019
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
Walter Roberson on 22 Dec 2019
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.

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