I have the following expression
FullSimplify[
Sqrt[1 + (-1 + a) (-1 + b) + 2 Sqrt[(-1 + a) (-1 + b)]] - Sqrt[
2 + a (-1 + b) - 2 Sqrt[(-1 + a) (-1 + b)] - b]]
Where $a\ge1$ and $b\ge1$. I know the answer should be $\sqrt{(1-a)(1-b)}$. However, $Mathematica$ doesn't solve this expression this way. How can one resolve this?
Reduce[{Sqrt[1 + (-1 + a) (-1 + b) + 2 Sqrt[(-1 + a) (-1 + b)]] - Sqrt[2 + a (-1 + b) - 2 Sqrt[(-1 + a) (-1 + b)] - b] == Sqrt[(a - 1) (b - 1)], a > 1, b > 1}]
says this isTrue
only whena == (3 + b)/(-1 + b)
$\endgroup$ – kglr Feb 19 '19 at 9:28a -> 1.23, b -> 2.34
. $\endgroup$ – b.gates.you.know.what Feb 19 '19 at 9:28