Question 6. The goal of this exercise is to make sure you understand √x² = ]x] and in general √x² ‡x. a) to find the fact that for any real number a such that a > 0, there is a unique number √a ≥ 0. Which fact is that? b) Evaluate the following (write them without square root): √(-5)² : (–a)² If a > 0: √a² √52 c) Bob is trying to prove an inequality. After few steps he got (a²b² + c²d²)² ≥ 4a²b²c²d². The only assumption on a, b, c and d is that they are real numbers. For the next step Bob took square root from both sides of the inequality and he got: (a²b² + c²d²) ≥ 2abcd. What is wrong?
Question 6. The goal of this exercise is to make sure you understand √x² = ]x] and in general √x² ‡x. a) to find the fact that for any real number a such that a > 0, there is a unique number √a ≥ 0. Which fact is that? b) Evaluate the following (write them without square root): √(-5)² : (–a)² If a > 0: √a² √52 c) Bob is trying to prove an inequality. After few steps he got (a²b² + c²d²)² ≥ 4a²b²c²d². The only assumption on a, b, c and d is that they are real numbers. For the next step Bob took square root from both sides of the inequality and he got: (a²b² + c²d²) ≥ 2abcd. What is wrong?
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 6. The goal of this exercise is to make sure you understand √x²
√x² ‡x.
a)
to find the fact that for any real number
there is a unique number √a ≥ 0. Which fact is that?
b) Evaluate the following (write them without square root): √(−5)²
√(-a)²
If a > 0: √a²
Jx] and in general
a such that a ≥ 0,
What is wrong?
√5²
c) Bob is trying to prove an inequality. After few steps he got (a²b² + c²d²)² ≥ 4a²b²c²d². The only
assumption on a, b, c and d is that they are real numbers. For the next step Bob took square root
from both sides of the inequality and he got:
(a²b² + c²d²) ≥ 2abcd.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe21e67d9-a430-46e1-bdb1-4a5d7c93d60c%2F127f5416-07be-4004-bedc-6a28b2f1de4b%2Fcg7e7wv_processed.png&w=3840&q=75)
Transcribed Image Text:Question 6. The goal of this exercise is to make sure you understand √x²
√x² ‡x.
a)
to find the fact that for any real number
there is a unique number √a ≥ 0. Which fact is that?
b) Evaluate the following (write them without square root): √(−5)²
√(-a)²
If a > 0: √a²
Jx] and in general
a such that a ≥ 0,
What is wrong?
√5²
c) Bob is trying to prove an inequality. After few steps he got (a²b² + c²d²)² ≥ 4a²b²c²d². The only
assumption on a, b, c and d is that they are real numbers. For the next step Bob took square root
from both sides of the inequality and he got:
(a²b² + c²d²) ≥ 2abcd.
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