Prove the following statements by contradiction If x is rational, x + cubed root of 2 is irrational. [Hint. Use the fact that the cubed is irrational, which has been proven in the text.]
Prove the following statements by contradiction If x is rational, x + cubed root of 2 is irrational. [Hint. Use the fact that the cubed is irrational, which has been proven in the text.]
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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Question
Prove the following statements by contradiction
If x is rational, x + cubed root of 2 is irrational. [Hint. Use the fact that the cubed is irrational, which has been proven in the text.]
Expert Solution
Step 1
To prove the conditional statement , by the method of contradiction, use the following steps.
- Assume that .
- Derive the result, which is a contradiction.
- Hence, .
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