System cannot be solved by Solve?

Questions
, ,
1

p[q_] := q^-[Delta];
Solve[q + (p[q] - [Tau])/p’[q] == 0 &&
1 > [Delta] > 0 && [Tau] > 0 && q > 0, q]

The solution I expect is

q = ((1 - \[Delta])/\[Tau])^(1/\[Delta])

However, I just get “This system cannot be solved with the methods available to Solve”. Any ideas why? Thanks.

2

Try:

  p[q_] := q^-\[Delta];
  Solve[q + (p[q] - \[Tau])/p'[q] == 0, q]

  (*{{q -> 0}, {q -> (-((-1 + \[Delta])/\[Tau]))^(1/\[Delta])}}*)

Solved on Mathematica 13.2.0.

3

Thanks for the reply; same error message here.
I’m absolutely clueless why that is.

4

This is a warnings message not errors .

Is about:

1.This message is generated when Solve and related functions use inverse functions to represent a solution.

2.Inverse functions normally give one branch of a general inverse, so equations that are solved in terms of inverse functions may omit solutions associated with other branches.