Question 2. Chun starts with numbers a, b ≥ 0 and puts them on a line. Then they draw a semi-circle with diameter a + b, and draw a vertical line of length c as in the diagram. a b (1) Assuming a + b is always the same number (but a and b can change), what is the smallest possible value of c you can get? What happens to a and b when that happens? What is the largest possible value of c you can get (as a function of a and b)? What relationship do a and b have when that happens? (2) Using geometry, show that c² = ab. (Hint: You may use the fact that the angle a in the diagram is always 90 degrees.) (3) Based on your work from parts 1 and 2 you have just proved a very important inequality. Write down that inequality.
Question 2. Chun starts with numbers a, b ≥ 0 and puts them on a line. Then they draw a semi-circle with diameter a + b, and draw a vertical line of length c as in the diagram. a b (1) Assuming a + b is always the same number (but a and b can change), what is the smallest possible value of c you can get? What happens to a and b when that happens? What is the largest possible value of c you can get (as a function of a and b)? What relationship do a and b have when that happens? (2) Using geometry, show that c² = ab. (Hint: You may use the fact that the angle a in the diagram is always 90 degrees.) (3) Based on your work from parts 1 and 2 you have just proved a very important inequality. Write down that inequality.
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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Transcribed Image Text:In this question you will practice combining algebra and geometry. These skills will be especially important in
Chapter 4 (applications of derivatives).
Question 2. Chun starts with numbers a, b ≥ 0 and puts them on a line. Then they draw a semi-circle with
diameter a + b, and draw a vertical line of length c as in the diagram.
a
(1) Assuming a + b is always the same number (but a and b can change), what is the smallest possible value
of c you can get? What happens to a and b when that happens? What is the largest possible value of c
you can get (as a function of a and b)? What relationship do a and b have when that happens?
(2) Using geometry, show that c² = ab. (Hint: You may use the fact that the angle a in the diagram is always
90 degrees.)
(3) Based on your work from parts 1 and 2 you have just proved a very important inequality. Write down that
inequality.
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