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You can use the fact that y2 is irrational to answer the questions below. You can also use other facts proven within this exercise. (a) Prove that V2/2 is irrational. (b) Prove that 2 – V2 is irrational. (c) Is it true that the sum of two positive irrational numbers is also irrational? Prove your answer. (d) Ie it truo that the product of two irrotional pumbore is olse irrotional2 Dro VOur nnnwor

You can use the fact that y2 is irrational to answer the questions below. You can also use other facts proven within this exercise. (a) Prove that V2/2 is irrational. (b) Prove that 2 – V2 is irrational. (c) Is it true that the sum of two positive irrational numbers is also irrational? Prove your answer. (d) Ie it truo that the product of two irrotional pumbore is olse irrotional2 Dro VOur nnnwor

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...
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You can use the fact that v2 is irrational to answer the questions below. You can also use other facts proven within this exercise. (a) Prove that V2/2 is irrational. (b) Prove that 2 V2 is irrational. (c) Is it true that the sum of two positive irrational numbers is also irrational? Prove your answer. (d) Is it true that the product of two irrational numbers is also irrational? Prove your answer. (e) Is the following statement true? Prove your answer. If x is a non-zero rational number and y is an irrational number, then y/x is irrational.
Transcribed Image Text:You can use the fact that v2 is irrational to answer the questions below. You can also use other facts proven within this exercise. (a) Prove that V2/2 is irrational. (b) Prove that 2 V2 is irrational. (c) Is it true that the sum of two positive irrational numbers is also irrational? Prove your answer. (d) Is it true that the product of two irrational numbers is also irrational? Prove your answer. (e) Is the following statement true? Prove your answer. If x is a non-zero rational number and y is an irrational number, then y/x is irrational.
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