Pre-Calculus Homework Solutions 133

Pre-Calculus Homework Solutions 133 - 33. Proof: Step 1...

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135 Chapter 5 33. Proof: Step 1 Assume that Ï 2 w is a rational number. Step 2 If Ï 2 w is a rational number, it can be written as } a b } ,where a and b are integers with no common factors, and b Þ 0. If Ï 2 w 5 } a b } ,then 2 5 } a b 2 2 } , and 2 b 2 5 a 2 .Thus a 2 is an even number, as is a .Because a is even it can be written as 2 n . 2 b 2 5 ¬ a 2 2 b 2 5 ¬ (2 n ) 2 2 b 2 5 ¬ 4 n 2 b 2 5 ¬ 2 n 2 b 2 is an even number. So, b is also an even number. Step 3 Because b and a are both even numbers, they have a common factor of 2. This contradicts the definition of rational numbers. Therefore, Ï 2 w is not rational. 34. Sample answer: Indirect proof is sometimes used in mystery novels. Answers should include the following. • Sherlock Holmes would disprove all possibilities except the actual solution to a mystery. • medical diagnosis, trials, scientific research 35. D; x 1 80 5 ¬ 140 x 5 ¬ 60 A, B, and C are true. D is not true. 36.
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