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A N Niel wrote:
>
> Wrong in general.
> Take a case where everything is rational...
>
> x1 = -3, x2 = -2, x3 = 0
> a = -1/4, b = 1/2
> n = 2, m = 1
>
> Then
> ax^3 + (a - 1)x^2 - (b + 1)x + 1 - 2b = a(x-x1)(x-x2)(x-x3)
> y1 = 1, y2 = 1
> but
> (2n+1)a^2+(3m+1)a+1 = 3y1^2+3y1y2+y2^2
> fails.
Thanks Niel, nice of you to verify the equation!
I made a mistake putting together the quadratic form.
This one should work out just fine:
((3n+1)a^2+(3m+1)a+1)/a^2=3y1^2+3y1y2+y2^2
which equals to 1.75 for your example.
Regards
Gerry
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