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Example 3 Find a Pythagorean triplet in which one member is 12. We know 2m, π‘š^2βˆ’1 and π‘š^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’Ž^πŸβˆ’πŸ" = 12" π‘š^2 = 12 + 1 π‘š^2 = 13 Since, 13 is not a square number, ∴ π‘š^2βˆ’1 β‰  12 It is not possible. Let π’Ž^𝟐+𝟏 = 12 π‘š^2 = 12 βˆ’ 1 π‘š^2 = 11 Since, 11 is not a square number, ∴ π‘š^2+1 β‰  12 It is not possible. Therefore, m = 6 Finding Triplets for m = 6 1st number = 2m 2nd number = π‘š^2βˆ’1 3rd number = π‘š^2+1 ∴ The required triplet is 12, 35, 37

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.