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Prove directly (without stating 7.10 from the chapter notes) that √2 + √5 is not rational.

Prove directly (without stating 7.10 from the chapter notes) that √2 + √5 is not rational.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Your answer to question 4 should be prepared in LATEX. 1. For each of the statement below, decide whether it is true or false, and prove your claim. (a) For all a, b € R, if a € Q \ {0} and b & Q then † ‡ Q. (b) For all x, y € R, if x is irrational and y is positive and irrational, then x + √y is irrational. 2. Prove that √10 is not rational without using the Fundamental Theorem of Arithmetic. 3. Prove that V12 is irrational using the Fundamental Theorem of Arithmetic. 4. Prove directly (without stating 7.10 from the chapter notes) that √√2 + √√5 is not rational. 5. Consider the following statement: For all r EQ, SER, rs is rational (i) Which of “if”, “only if”, “iff” in claim. (ii) Which of "if", "only if", "iff” in claim. s is rational. make this a true statement? Prove your make this a false statement? Prove your
Transcribed Image Text:Your answer to question 4 should be prepared in LATEX. 1. For each of the statement below, decide whether it is true or false, and prove your claim. (a) For all a, b € R, if a € Q \ {0} and b & Q then † ‡ Q. (b) For all x, y € R, if x is irrational and y is positive and irrational, then x + √y is irrational. 2. Prove that √10 is not rational without using the Fundamental Theorem of Arithmetic. 3. Prove that V12 is irrational using the Fundamental Theorem of Arithmetic. 4. Prove directly (without stating 7.10 from the chapter notes) that √√2 + √√5 is not rational. 5. Consider the following statement: For all r EQ, SER, rs is rational (i) Which of “if”, “only if”, “iff” in claim. (ii) Which of "if", "only if", "iff” in claim. s is rational. make this a true statement? Prove your make this a false statement? Prove your
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