4. [Disproof by Counter Example] Prove that the following statements are false. a) x²=4 => x=2. b) For all real values of a and b, a-b>0 a²-b² >0. c) The sum of two unequal, positive, irrational numbers is irrational. d) The product of two unequal, positive, irrational numbers is irrational.
4. [Disproof by Counter Example] Prove that the following statements are false. a) x²=4 => x=2. b) For all real values of a and b, a-b>0 a²-b² >0. c) The sum of two unequal, positive, irrational numbers is irrational. d) The product of two unequal, positive, irrational numbers is irrational.
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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![4. [Disproof by Counter Example]
Prove that the following statements are false.
a) x² = 4 ⇒x=2.
b) For all real values of a and b, a-b>0
a²-b² >0.
c) The sum of two unequal, positive, irrational numbers is irrational.
d) The product of two unequal, positive, irrational numbers is irrational.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0df03678-79d5-4fc1-8c77-0bce24101430%2F0b4a8443-baf0-4f37-b63c-bda9ad4dab15%2F5qsxx1t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. [Disproof by Counter Example]
Prove that the following statements are false.
a) x² = 4 ⇒x=2.
b) For all real values of a and b, a-b>0
a²-b² >0.
c) The sum of two unequal, positive, irrational numbers is irrational.
d) The product of two unequal, positive, irrational numbers is irrational.
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