Write a Pythagorean triplet whose smallest member is:
(i) 6 (ii) 14 (iii) 16 (iv) 20
(i) As we know that,
For every number m > 1, the Pythagorean triplet is (2m, m2 – 1, m2 + 1)
Using this result in the question, we get
2m = 6
m = 3
m2 = 9
m2 – 1 = 9 – 1 = 8
m2 + 1 = 9 + 1 = 10
Thus,
The Pythagorean triplet is [6, 8, 10]
(ii) As we know that,
For every number m > 1, the Pythagorean triplet is (2m, m2 – 1, m2 + 1)
Using this result in the question, we get
2m = 14
m = 7
m2 = 49
m2 – 1 = 49 – 1 = 48
m2 + 1 = 49 + 1 = 50
Thus,
The Pythagorean triplet is [14, 48, 50]
(iii) As we know that,
For every number m > 1, the Pythagorean triplet is (2m, m2 – 1, m2 + 1)
Using this result in the question, we get
2m = 16
m = 8
m2 = 64
m2 – 1 = 64 – 1 = 63
m2 + 1 = 64 + 1 = 65
Thus,
The Pythagorean triplet is [16, 63, 65]
(iv) As we know that,
For every number m > 1, the Pythagorean triplet is (2m, m2 – 1, m2 + 1)
Using this result in the question, we get
2m = 20
m = 10
m2 = 100
m2 – 1 = 100 – 1 = 99
m2 + 1 = 100 + 1 = 101
Thus,
The Pythagorean triplet is [20, 99, 101]