Let m ∈ N.
(a) Prove that m2 – 1, 2m, m2 + 1 is a Pythagorean triple.
(b) Show that not all Pythagorean triples given by expression in part (a) are primitive.
(c) Show that not all Pythagorean triples given by the expression in part (a).
Answers
Answered by
24
➡️ (m^2 + 1)^2 = (m^2 - 1)^2 + (2m)^2
Or, (m^2 + 1)^2 - (m^2 - 1)^2 = 4m^2
Or, 4m^2 = 4m^2
Hence, verified.
➡️ However, (5, 12, 13) is a Pythagorean triplet that is not in this form.
That's it..
Answered by
20
➡️ (m^2 + 1)^2 = (m^2 - 1)^2 + (2m)^2
Or, (m^2 + 1)^2 - (m^2 - 1)^2 = 4m^2
Or, 4m^2 = 4m^2
Hence, verified.
♞However, (5, 12, 13) is a Pythagorean triplet that is not in this form.
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