Re: [Maxima-discuss] Another solve toughie

[Raymond T. <toy...@gm...>]

On 3/4/26 1:52 PM, Richard Fateman wrote:

> solve( y =  (sqrt(4*x+1)-sqrt(x+1))/(sqrt(9*x+1)-sqrt(x+1)) , x);
>
> a solution is x= -((4*(y-1)*y*(8*y-3))/((2*y-1)*(2*y+3)*(4*y-3)*(4*y+1)))
|to_poly_solve| produces an answer after a bit of time. It's really 
messy, so I'm not pasting it here. But it does, after calling |factor|, 
produce the same answer as you give, with lots of conditions on the 
value of y.
>
> a challenge might also be:  prove that
> f(x) := if x=0 then 3/8 else 
> (sqrt(4*x+1)-sqrt(x+1))/(sqrt(9*x+1)-sqrt(x+1))
> is continuous everywhere.
How can that be true? sqrt(x+1) isn't continuous everywhere for real x.
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