Answer:
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)
