Cas.solve Problem

[megamanu]

(08-15-2024 06:45 PM)Albert Chan Wrote:  

(08-14-2024 05:37 AM)ftneek Wrote:  The trouble is likely the size of the constants in this equation ...
where the constants are large, or in general, its a good idea to try and solve symbolically first

What is large? It is all relative, depends on how we define the problem.

Cas> solve(x = sqrt(1-(a*x)^2))                    → []
Cas> solve(x = sqrt(1-(a*x)^2) * b) (b=1)     → {1/√(a^2+1)}

Here, even implied multiply (by 1) need symbol b, is 1 too large?
What about the 1 inside square root ... is that too large too?

I wish solver can figure this out, without user decide what constants need to be symbolic.
In the meantime, remove square root is the way to go, allow solver to recognize quadratic.

Cas> solve(x^2 = (1-(a*x)^2) AND x>=0)     → {1/√(a^2+1)}

So, what do you recommend me to do in this case? Solve it simbolically as the other user said?