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Unformatted text preview: n N such that q i = 0 for all i n . Find the cardinality of S . (5) Show that p 2 + 3 and 1 2+ 3 are algebraic. Extra Credit: Show that 3 2 + 3 3 is irrational. Hint: First show that x = 3 2 + 3 3 is algebraic by constructing an explicit polynomial f ( x ) with integer coecients such that f ( x ) = 0. then prove that f ( x ) has no rational roots. 1...
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 Spring '10
 Applebaugh
 Math

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