Example 3 Find a Pythagorean triplet in which one member is 12.
We know 2m, π^2β1 and π^2+1 form a Pythagorean triplet.
Given,
One member of the triplet = 12.
Let 2m = 12
2m = 12
m = 12/2
m = 6
Let π^πβπ" = 12"
π^2 = 12 + 1
π^2 = 13
Since, 13 is not a square number,
β΄ π^2β1 β 12
It is not possible.
Let π^π+π = 12
π^2 = 12 β 1
π^2 = 11
Since, 11 is not a square number,
β΄ π^2+1 β 12
It is not possible.
Therefore, m = 6
Finding Triplets for m = 6
1st number = 2m
2nd number = π^2β1
3rd number = π^2+1
β΄ The required triplet is 12, 35, 37

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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