Question

2) The triplet of Pythagoras can be obtained in the following manner. For the
first triplet of Pythagoras by putting n=1 in the following formulae, we get,
i) m = 2n + 1 = 3.
ii) m2-1
3² – 1
8.
-
4
2.
2
2
m2 + 1
3² + 1
10
HI
= 5
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.​

Answer 1

Solution :-

A triplet is in the form :-

• m = 2n + 1
• m² - 1
• m² + 1

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 .