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From: Raymond T. <toy...@gm...> - 2026-03-04 22:40:12
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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. ​ |