Concept explainers
(a)
To prove: the polynomial identity is true by showing that the simplified expressions for the left and right sides are the same.
(a)
Answer to Problem 65E
The identify is true
Explanation of Solution
Given information:
A Pythagorean triple is a set of positive integers
Calculation:
Expand and simplify the expression on the left side of equation.
Expand and simplify the expression on the left side of equation.
Because the simplified left side is equal to the right side, so the identify is true.
(b)
To generate: the Pythagorean triple when
(b)
Answer to Problem 65E
The Pythagorean triplets are 11, 60 and 61.
Explanation of Solution
Given information:
A Pythagorean triple is a set of positive integers
Calculation:
Use the identity when
Therefore, the Pythagorean triplets are 11, 60 and 61.
(c)
To verify: the answer in part (b) satisfies
(c)
Answer to Problem 65E
Explanation of Solution
Given information:
A Pythagorean triple is a set of positive integers
Calculation:
Using
Thus, result in part (b) satisfies
Chapter 4 Solutions
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