cannot solve simple equation

[nickapos]

(11-24-2023 08:34 PM)Albert Chan Wrote:  

(11-24-2023 07:20 PM)nickapos Wrote:  Why it does not work with 4.1 and it does work with 41/10?

With exact number, solve does it symbolically.
It is equivalent to solve with symbols, then substitute for answer.

Cas> solve(a = b/sqrt(1-(v/c)^2), v) (a=4.1, b=2.6, c=3e8)

{231963914.402, −231963914.402}

With float, solver use Newton's method, but guess (v=tan(t), t = ±1.57) is too low.
There is no measurable relativistic effect, the region examined is just a flatline.

Cas> f(v) := 4.1 - 2.6 / sqrt(1-(v/3e8)^2)
Cas> f(tan(−1.57))      → 1.49999999998
Cas> f(0)                    →   1.5
Cas> f(tan(+1.57))      → 1.49999999998

We have to provide a better guess for v

Cas> solve(f(v), v=2e8)      → 231963914.402

Thank you very much Albert that makes sense