Am I missing something here? This does not resolve to True.
Clear[x,y]
$Assumptions={x>0,y>0}
FullSimplify[(Sqrt[x] + Sqrt[y]) == Sqrt[x + y + 2 Sqrt[x y]]]
$\begingroup$
$\endgroup$
2
1 Answer
$\begingroup$
$\endgroup$
Resolve[ForAll[{x, y},
Sqrt[x] + Sqrt[y] == Sqrt[x + y + 2 Sqrt[x y]]], PositiveReals]
True
Simplify[Reduce[{(Sqrt[x] + Sqrt[y]) == Sqrt[x + y + 2 Sqrt[x y]], x > 0 && y > 0}], {x > 0, y > 0}]$\endgroup$SimplifybecauseReduce[(Sqrt[x] + Sqrt[y]) - Sqrt[x + y + 2 Sqrt[x y]] == 0, Reals]givesy >= 0 && x >= 0, thereforeSimplifywith this assumption should giveTruebut it does not. $\endgroup$