A bug or not in Equation solver?

Questions
,
1

In[6]:= Solve[-3 (y - 2)^(4/5) + 29 == -19, y, Integers]

Out[6]= {{y -> 34}}

There is another root for above equation that is y → -30. But the software only display one root. Is it a bug?

2

You can use Surd to also get the negative real root:

Solve[-3 Surd[(y - 2)^4, 5] + 29 == -19, y]
(* {{y -> -30}, {y -> 34}} *)

As an alternative the equation can be rewritten:

Solve[-3 ((y - 2)^4)^(1/5) + 29 == -19, y, Integers]
(* {{y -> -30}, {y -> 34}} *)
3

Thanks for the help.