Cas.solve Problem

[C.Ret]

(08-14-2024 01:37 AM)megamanu Wrote:  Do you know why the hp prime cant solve it with the numbers directly instead of the symbols?

Our messages crossed. Consider this answer as a complement to the arguments given by ftneek. May he feel free to complete or correct my answer.

The fact that the HP Prime does not find a solution to this equation in CAS mode while it finds a symbolic one comes from the very foundation of a CAS system. In CAS mode, the SOLVE instruction will give a symbolic solution no matter what.

On the other hand, if the equation is only numerical then, for convenience, this same SOLVE instruction will attempt a numerical approach. Hence the display of the intermediate screen.
Unlike other resolution instructions present elsewhere in other applications of the HP Prime, its numerical range is narrower in CAS (a consequence linked to the implementation of it) and above all strongly dependent on the initial conditions.

If the user enters a purely symbolic expression to the equation in CAS.SOLVE, there is no ambiguity and the symbolic approach will give a symbolic answer.
On the other hand, a problem arises if the user gives numerical values ​​to the equation to be solved without specifying any initial value for the numerical search. Unlike the SOLVE instructions of specific applications, the absence of an initial value often does not lead to any result.

On the following screenshot, I illustrate two approaches allowing a numerical result in CAS mode. The first suggested by ftneek is done in two steps, the first of which requires the enumeration of the symbolic solutions.
As well as an alternative method that leaves the choice to the CAS system of the method but without forgetting to give the unknown x a coherent initial value facilitating the numerical resolution.



Of course, the numerical method can lead to approximate results. While the symbolic method will give more precise and more accurate results.
Here, only the symbolic method gives 299999999.966, the numerical method results in 3*10⁸.


Hoping that this helps a little.
Kind regards.