Consider the following theorem: There do not exist three consecutive odd integers a, b and c such that a² + b² = c². Example of three consecutive odd integers can be 1,3,5. a) Restate the theorem into a conditional statement or implication (p⇒q): If a,b and c are consecutive odd integers, then a^2 c^2. Put your answer in the blank as "is equal to" or "isn't equal to". +b^2 b) Fill in the blanks in the following proof of the theorem. Proof: Let a,b, and c be consecutive odd integers. Then a=2k+1, b= Suppose a² + b² = c². Then (2k + 1)²+1 and c=2k+5 for some integer k. )^2=(2k+5)². =0. Thus, k = or k= If follows that 8k² + 16k + 10 = 4k² + 20k + 25 and 4k² - 4k- This contradicts k being an Therefore, there does not exist three consecutive odd integers a,b and c such that a² + b² = c².
Consider the following theorem: There do not exist three consecutive odd integers a, b and c such that a² + b² = c². Example of three consecutive odd integers can be 1,3,5. a) Restate the theorem into a conditional statement or implication (p⇒q): If a,b and c are consecutive odd integers, then a^2 c^2. Put your answer in the blank as "is equal to" or "isn't equal to". +b^2 b) Fill in the blanks in the following proof of the theorem. Proof: Let a,b, and c be consecutive odd integers. Then a=2k+1, b= Suppose a² + b² = c². Then (2k + 1)²+1 and c=2k+5 for some integer k. )^2=(2k+5)². =0. Thus, k = or k= If follows that 8k² + 16k + 10 = 4k² + 20k + 25 and 4k² - 4k- This contradicts k being an Therefore, there does not exist three consecutive odd integers a,b and c such that a² + b² = c².
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Consider the following theorem: There do not exist three consecutive odd integers a, b and c such that a² + b² = c². Example of
three consecutive odd integers can be 1,3,5.
a) Restate the theorem into a conditional statement or implication (p⇒q): If a,b and c are consecutive odd integers, then a^2
c^2. Put your answer in the blank as "is equal to" or "isn't equal to".
+b^2
b) Fill in the blanks in the following proof of the theorem.
Proof: Let a,b, and c be consecutive odd integers. Then a=2k+1, b=
Suppose a² + b² = c². Then (2k + 1)²+1
and c=2k+5 for some integer k.
)^2=(2k+5)².
=0. Thus, k = or k=
If follows that 8k² + 16k + 10 = 4k² + 20k + 25 and 4k² - 4k-
This contradicts k being an
Therefore, there does not exist three consecutive odd integers a,b and c such that a² + b² = c².
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
