Generate six pythagorean triples using any method discussed during class. explain each method you use.

1) (3,4,5)

2) (6,8,10)

3) (8,15,17)

4) (10,24,26)

5) (5,12,13)

6) (33,56,65)

Step-by-step explanation:

There are many ways of generating Pythagorean triples (a,b,c), one of the easiest ones is to take two natural numbers n and m, and we will have:

a = n² - m²,

b = 2nm,

c = n² + m²

Then (a, b, c) is a Pythagorean triple.

So, we're going to generate 6 Pythagorean triples using this method.

1. m= 1 and n = 2

⇒a = 2² - 1² = 3

b =2(1)(2) = 4

c= 1² + 2² = 5

and the triple is (3,4,5)

2. Now for m = 1 and n = 3

⇒a = 3²-1² = 8

b= 2(3)(1) =6

c = 1²+3² = 10

and the triple is (6,8,10)

3. Now for m = 1 and n = 4

⇒a = 4²-1²=15

b=2(1)(4)=8

c= 4²+1²=17

And the triple is (8,15,17)

4. Now for m = 1 and n =5

⇒a = 5²-1²=24

b=2(1)(5)=10

c= 5²+1²=26

and the triple is (10,24,26)

5. m = 2 n = 3

⇒a = 3²-2²= 5

b= 2(2)(3)=12

c= 3²+2²= 13

And the triple is (5,12,13)

6. m= 4 n = 7

⇒a= 7²-4²=33

b=2(7)(4)=56

c= 4²+7²= 65

And the triple is (33,56,65)

bn,mn,n.vn.

step-by-step explanation:

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00