orem 1. If a and b are positive real numbers, then a+b 2 of. questions. Your task is to say what's wrong with the pre 介介介介介 > √ab. a+b 2 (a + b)² ab 2 (a + b)² ≥ 4ab a² + 2ab + b² > 4ab a² - 2ab + b² > 0 (a - b)² ≥ 0 mich is true, because any number squared is > 0. ab L
orem 1. If a and b are positive real numbers, then a+b 2 of. questions. Your task is to say what's wrong with the pre 介介介介介 > √ab. a+b 2 (a + b)² ab 2 (a + b)² ≥ 4ab a² + 2ab + b² > 4ab a² - 2ab + b² > 0 (a - b)² ≥ 0 mich is true, because any number squared is > 0. ab L
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question

Transcribed Image Text:As we start thinking about proofs, a good thing to try to do is to find the mistakes with incorrect
proofs. Here's an example from old exam questions. Your task is to say what's wrong with the proof.
Theorem 1. If a and b are positive real numbers, then a+b
2
Proof.
> √ab.
a+b
2
(a + b)²
2
(a + b)² ≥ 4ab
a² + 2ab + b² > 4ab
a² - 2ab + b² > 0
(a - b)² ≥ 0
which is true, because any number squared is > 0.
> √ab
> ab
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