Result from solve() command shows c_0

[jfdHP]

@parisse Thaks for the response. I do agree.

Thinking about this issue, I found another (simple) example about the problem of simplifying square roots.
Try
simplify(sqrt(x^2-6*x*sqrt(x-2)+9*x-18)
We obtain (with HP prime - I checked that XCas provides the same answer) :
3*|sqrt(x-2)| - |x|*sign(x)
A priori this is a very nice result, because the CAS understood that there was a not obvious simplification. For comparison, in that example Wolfram alpha or Maple 14 are not able to simplify anything. Considering the fact that a square root is always positive, the CAS could have given the simpler equivalent result 3*sqrt(x-2) - x but this is not a big problem.

The problem is that the answer is not correct for any value of x. In fact we have x^2-6*x*sqrt(x-2)+9*x-18 = (x-3*sqrt(x-2))^2 so that the general solution is in fact
|x-3*sqrt(x-2)|
Thus the result given by the CAS is valid only when 3*sqrt(x-2) - x > 0 , i.e. for 3 < x < 6. Elsewhere, there is a sign problem.

Thus it is surprising to see that the CAS finds the simplification trick, which is not obvious at all, but it did not succeed in managing the sign issue whereas a priori (for a human being), it is much simpler in this example. For practical use, I would say that this sign issue is a little bit more serious than the solve question because we know for solve that a universal solver does not exist so that we have to be cautious with the given solutions, but for a relatively simpler simplification it is a little bit more surprising.