Math, asked by godurobo, 11 months ago

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 arnab2261
24

 {\huge {\mathfrak {Answer :-}}}

➡️ (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 Soumok
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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