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Unformatted text preview: a + b 2 + c 3 = 0 . Prove that a = b = c = 0. (b) Let a, b, c, d be rational and a + b = c + d. Prove that either a = c and b = d or b and d are squares of rationals. (c) Let a, b, c, d be rational and x be irrational. In what circumstances is ax + b cx + d rational? 6. Using the axioms of real numbers show that (a) ( a R )( b R )( c R )[(( ac = ab ) ( a 6 = 0)) = ( b = c )]; (b) ( a R )( b R )[(-a )(-b ) = ab ]; (c) ( a R )( b R )( c R )[(( a > b ) ( c < 0)) = ( ac < bc )]....
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This note was uploaded on 02/25/2010 for the course MATHEMATIC 11007 taught by Professor Spyros during the Winter '10 term at Bristol Community College.
- Winter '10