How many of the following are Pythagorean triplets ?
[8, 15, 17], [13, 60, 61], [14, 48, 50). [11, 40, 41).
Explain it!

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1. Question :-

   To find which of the following are Pythagorean triplets.

   Answer :-

   Concept :-

   According to the Pythagorean triplet, the three numbers are in the form as follows :-

   • 2m
   • m² – 1
   • m² + 1

   2m being the smallest number

   Option 1 :-

   ➵ 8,15,17

   In this set, 8 is the smallest number.

   Therefore,

   → 2m = 8

   → m = 8 ÷ 2

   → m = 4

   Now that we have the value of m, the other 2 numbers will be :-

   → m² – 1

   → (4)² – 1

   → 16 – 1

   → 15

   The third number :-

   → m² + 1

   → (4)² + 1

   → 16 + 1

   → 17

   All the answer’s are matching the set. Hence, 8,15,17 is a Pythagorean triplet.

   Option 2 :-

   ➵ 13,60,61

   Here, the smallest number is 13.

   → 2m = 13

   13 is not exactly divisible by 2. Hence this triplet cannot be formed.

   Option 3 :-

   ➵ 14,48,50

   Here 14, is the smallest number.

   Therefore,

   → 2m = 14

   → m = 14 ÷ 2

   → m = 7

   Second number :-

   → m² – 1

   → (7)² – 1

   → 49 – 1

   → 48

   Third number :-

   → m² + 1

   → (7)² + 1

   → 49 + 1

   → 50

   All the numbers are matching the set, hence 14,48,50 is a Pythagorean triplet

   Option 4 :-

   ➵ 11,40,41

   → 2m = 11

   Here 11 is not exactly divisible by 2. Hence the triplet cannot be formed.

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