i. Let a = 2, b = 1
a2 + b2 = 22 + 12 = 4 + 1 = 5
a2 – b2 = 22 – 12 = 4 – 1 = 3
2ab = 2 × 2 × 1 = 4
∴ (5, 3, 4) is a Pythagorean triplet.
ii. Let a = 4,b = 3
a2 + b2 = 42 + 32 = 16 + 9 = 25
a2 – b2 = 42 – 32 = 16 – 9 = 7
2ab = 2 × 4 × 3 = 24
∴ (25, 7, 24) is a Pythagorean triplet
iii. Let a = 5, b = 2
a2 + b2 = 52 + 22 = 25 + 4 = 29
a2 – b2 = 52 – 22 = 25 – 4 = 21
2ab = 2 × 5 × 2 = 20
∴ (29, 21, 20) is a Pythagorean triplet.
iv. Let a = 4,b = 1
a2 + b2 = 42 + 12 = 16 + 1 = 17
a2 – b2 = 42 – 12 = 16 – 1 = 15
2ab = 2 × 4 × 1 = 8
∴ (17, 15, 8) is a Pythagorean triplet.
v. Let a = 9, b = 7
a2 + b2 = 92 + 72 = 81 + 49 = 130
a2 – b2 = 92 – 72 = 81 – 49 = 32
2ab = 2 × 9 × 7 = 126
∴ (130,32,126) is a Pythagorean triplet.
Note: Numbers in Pythagorean triplet can be written in any order.