Question

Find the Pythagorean triplets from among the following sets of numbers:

i. 2, 6, 7 

ii. 9, 40, 41 

iii. 4, 7, 8

Answer 1

i. 2² = 4, 6²  = 36, 7^{​​​​​​​2}  = 49 

But, 4 + 36 ≠ 49 

∴ 2^{​​​​​​​2}  + 6^{​​​​​​​2}  ≠ 7^{​​​​​​​2}  

∴ 2, 6 and 7 is not a Pythagorean triplet. 

ii. 9^{​​​​​​​2}  = 81, 40^{​​​​​​​2}  = 1600, 41^{​​​​​​​2}  = 1681 

Now, 81 + 1600 = 1681 

∴ 9^{​​​​​​​2}  + 40^{​​​​​​​2}  = 41^{​​​​​​​2}  

∴ 9,40 and 41 is a Pythagorean triplet. 

iii. 4^{​​​​​​​2}  = 16, 7^{​​​​​​​2}  = 49, 8^{​​​​​​​2}  = 64 

But, 16 + 49 ≠ 64 

∴ 4^{​​​​​​​2}  + 7^{​​​​​​​2}  ≠ 8^{​​​​​​​2}  

∴ 4, 7 and 8 is not a Pythagorean triplet.