The solution to this is ugly, right?

[Mitch Harris]

On Fri, May 30, 2008 at 12:04 PM, David W. Wilson <wilson.d at anseri.com> wrote:
> Solve (a-x)^(-1/2) + (b-x)^(-1/2) = 1 for x.
>
> The solution is an ugly quartic?

Mma helped me reduce this to:

a^2 + 6 a b - 2 a^2 b + b^2 - 2 a b^2 +  a^2 b^2 +
(-8 a + 2 a^2 - 8 b + 8 a b - 2 a^2 b + 2 b^2 - 2 a b^2) x +
(8 - 6 a + a^2 - 6 b + 4 a b + b^2) x^2 +
(4 - 2 a - 2 b) x^3 +
x^4
= 0

I'd have to say yes, ugly and quartic.

Mitch