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The rationalization of the expression
15+2+1\dfrac{1}{\sqrt{5} + \sqrt{2} + 1}5+2+11
can be expressed as
−A10−B5+C2+DE,\dfrac{- A\sqrt{10} - B\sqrt{5} + C\sqrt{2} + D}{E},E−A10−B5+C2+D,
where AAA, BBB, CCC, DDD, and EEE are all positive integers.
Find the minimum value of A+B+C+D+EA + B + C + D + EA+B+C+D+E.
This problem is part of the set "Xenophobia."
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