(a) Compute V178212+184112 by typing the following into MATLAB: format short (1782 12+ 1841-12) (1/12) CHAPTER 5 What result does MATLAB report? Now look at the answer using format long. (b) Determine the absolute and relative error in the approximation 178212+184112 192212. (Such an example is called a Fermat near miss because of the small relative error. This example was created by The Simpsons writer David S. Cohen with the intent of catching the eye of audience members with a mathematical interest.) c) Note that the right-hand side of equation (5.2) is even. Use this to prove that the equation cannot be true. d) In a later episode entitled The Wizard of Evergreen Terrace, Homer writes the equation 398712+4365¹2 = 447212. Can you debunk this equation?

(a) Compute V178212+184112 by typing the following into MATLAB: format short (1782 12+ 1841-12) (1/12) CHAPTER 5 What result does MATLAB report? Now look at the answer using format long. (b) Determine the absolute and relative error in the approximation 178212+184112 192212. (Such an example is called a Fermat near miss because of the small relative error. This example was created by The Simpsons writer David S. Cohen with the intent of catching the eye of audience members with a mathematical interest.) c) Note that the right-hand side of equation (5.2) is even. Use this to prove that the equation cannot be true. d) In a later episode entitled The Wizard of Evergreen Terrace, Homer writes the equation 398712+4365¹2 = 447212. Can you debunk this equation?

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

CHAPTER 5
(a) Compute 178212 +184112 by typing the following into MATLAB:
format short
(1782 12+ 1841-12) (1/12)
What result does MATLAB report? Now look at the answer using
format long.
(b) Determine the absolute and relative error in the approximation
178212+184112 1922¹2. (Such an example is called a Fermat near
miss because of the small relative error. This example was created by
The Simpsons writer David S. Cohen with the intent of catching the
eye of audience members with a mathematical interest.)
(c) Note that the right-hand side of equation (5.2) is even. Use this to
prove that the equation cannot be true.
(d) In a later episode entitled The Wizard of Evergreen Terrace, Homer
writes the equation 398712 +4365¹2 = 447212. Can you debunk this
equation?

will the correct answer be
13. In the 7th season episode Treehouse of Horror VI of The Simpsons,
Homer has a nightmare in which the following equation flies past him:
178212 +184112 = 192212.
(5.2)
Note that this equation, if true, would contradict Fermat's last theorem,
which states: For n ≥ 3, there do not exist any natural numbers x, y
2". Did Homer dream up a
and z that satisfy the equation x"+y":
counterexample to Fermat's last theorem?
=

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