SOLUTION: I need help. I do not understand any of this. I need to build or generate at least five more Pythagorean Triples using one of the many formulas available. After building your t

Question 635117: I need help. I do not understand any of this.
I need to build or generate at least five more Pythagorean Triples using one of the many formulas available. After building your triples, verify each of them in the Pythagorean Theorem equation. The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
Thank you for any help you can give me.
Found 2 solutions by richwmiller, ankor@dixie-net.com:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
There are 16 primitive Pythagorean triples with c ≤ 100:
( 3 , 4 , 5 ) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)
(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)
(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
generate at least five more Pythagorean Triples using one of the many formulas available.
After building your triples, verify each of them in the Pythagorean Theorem equation.
:
Euclid's formula for generating triples, given an arbitrary pair of positive
integers, m and n, where m > n. a^2 + b^2 = c^2
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
:
Choose numbers less than 10
Example1; m=3, n=2
a = 3^2 - 2^2 = 9 - 4 = 5
b = 2(3*2) = 12
c = 3^2 + 2^2 = 13
So we have a triple: 5, 12, 13
5^2 + 12^2 = 13^2
25 + 144 = 169
:
Example 2: m=7, n=3
a = 49-9 = 40
b = 2(7*3) = 42
c = 49 + 9 = 58
a=40, b=42, c=58
:
Example 3: m=9, m=5
a = 81 - 25 = 56
b = 2(9*5) = 90
c = 81 + 25 = 106
a=56, b=90, c = 106
:
You should be able to generate a few more using this method,
check them on your calc enter: to find c
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