Sorry for the vague title, but I wasn't sure how to phrase this.
I was using Mathematica to solve a fairly simple algebraic equation, but when I tried to substitute the solution into the original equation as a check, I can't seem to recover my original answer. Minimal example:
eq = a == (1 - b)/Sqrt[1 - 2 b]
sol = Solve[eq, b]
FullSimplify[(1 - b)/Sqrt[1 - 2 b] /. sol, a > 0]
The final line outputs
{(a (a + Sqrt[-1 + a^2]))/Sqrt[-1 + 2 a (a + Sqrt[-1 + a^2])], (a (a - Sqrt[-1 + a^2]))/Sqrt[-1 + 2 a (a - Sqrt[-1 + a^2])]}
even after I've specified that a is positive. So FullSimplify
is not enough to make this last line output a
. What am I missing?