2 The triplet or Pythagoras can be obtained in the following manner. For the
O first triplet of Pythagoras by putting in the following formulae, we get,
i) m – 2n +1 -3.
ii) m² – 1
2
2
2
10
32+1
m?+ 1
5
11
2
2
2
(3. 4. 5) is the first triplet of pythagoras (3, 4, 5) being the sides of
a right angled triangle. Similarly, find the third and fifth triplet of
Pythagoras by putting n=3 and n=5, in the above formulae.
Solution :-
A triplet is in the form :-
putting n = 3 :-
→ m = 2 * 3 – 1 = 6 – 1 = 5
→ m² – 1 = 5² – 1 = 25 – 1 = 24
→ m² + 1 = 5² + 1 = 25 + 1 = 26
so,
→ m² – 1 / m² + 1 = 24/26 = 12 / 13 .
therefore, (5,12,13) is the third triplet of Pythagoras .
putting n = 5 :-
→ m = 2 * 5 – 1 = 10 – 1 = 9
→ m² – 1 = 9² – 1 = 81 – 1 = 80
→ m² + 1 = 9² + 1 = 81 + 1 = 82
so,
→ m² – 1 / m² + 1 = 80/82 = 40 / 41 .
therefore, (9,40,41) is the third triplet of Pythagoras .