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Q.

Find a Pythagorean triplet whose one member is 14.

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a

6, 14 and 16

b

14, 46 and 50

c

14, 48 and 50

d

14, 42 and 45

answer is C.

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Detailed Solution

We know that the Pythagorean triplets can be found by using the general form 2m, m2 βˆ’ 1, m2 + 1, where m is a natural number greater than 1.

If m2 βˆ’ 1 = 14

β‡’ m2 = 14 + 1 = 15

Then, the value of m will not be an integer.

If m2 + 1 = 14

β‡’ m2 = 14 βˆ’ 1 = 13

Then, the value of m will not be an integer.

Therefore, let 2m = 14

β‡’ m = 7, which is a natural number greater than 1

∴ m2 βˆ’ 1 = 72 βˆ’ 1 = 49 βˆ’ 1 = 48,

m2 + 1 = 72 + 1 = 49 + 1 = 50.

Therefore, the required Pythagorean triplet is 14, 48 and 50.

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Find a Pythagorean triplet whose one member is 14.