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,...
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![### Pythagorean Identity and Triples
**Problem Statement:**
Given the values \( x \) and \( y \), use the Pythagorean Identity to create a set of Pythagorean Triples. Let \( x = 13 \), \( y = 6 \).
**Pythagorean Identity:**
\[
(x^2 - y^2)^2 + (2xy)^2 = (x^2 + y^2)^2
\]
**Choices for Possible Pythagorean Triples:**
- (49, 156, 205)
- (133, 90, 205)
- (49, 90, 205)
- (133, 156, 205)
**Explanation:**
Using the given formula and substituting \( x = 13 \) and \( y = 6 \), solve for the Pythagorean triples by calculating:
- \( x^2 - y^2 \)
- \( 2xy \)
- \( x^2 + y^2 \)
This set of calculations will yield a group of three numbers that satisfy the Pythagorean identity, forming a Pythagorean Triple. Choose the correct set from the options provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe4e0d9-a441-4076-9243-8e98c4a90bfe%2F9addd3b8-afaf-42e3-8d30-af3991a0b82e%2Fch2ym37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Pythagorean Identity and Triples
**Problem Statement:**
Given the values \( x \) and \( y \), use the Pythagorean Identity to create a set of Pythagorean Triples. Let \( x = 13 \), \( y = 6 \).
**Pythagorean Identity:**
\[
(x^2 - y^2)^2 + (2xy)^2 = (x^2 + y^2)^2
\]
**Choices for Possible Pythagorean Triples:**
- (49, 156, 205)
- (133, 90, 205)
- (49, 90, 205)
- (133, 156, 205)
**Explanation:**
Using the given formula and substituting \( x = 13 \) and \( y = 6 \), solve for the Pythagorean triples by calculating:
- \( x^2 - y^2 \)
- \( 2xy \)
- \( x^2 + y^2 \)
This set of calculations will yield a group of three numbers that satisfy the Pythagorean identity, forming a Pythagorean Triple. Choose the correct set from the options provided.
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