Too much roots!
Algebra
Level
4
The rationalization of the expression
\[\dfrac{1}{\sqrt{5} + \sqrt{2} + 1}\]
can be expressed as
\[\dfrac{- A\sqrt{10} - B\sqrt{5} + C\sqrt{2} + D}{E},\]
where \(A\), \(B\), \(C\), \(D\), and \(E\) are all positive integers.
Find the minimum value of \(A + B + C + D + E\).
This problem is part of the set "Xenophobia."
by
Rindell Mabunga