Either prove or disprove this mathematical claim detailed please problems use Pythagorean Theorem, assumed to be true without any proof: "Forany right triangle, if its legs have length a and b and its hypotenuse length c, then a² + b²c²." Inaddition, two additional definitions are relevant to the conjectures you choose from below: a Pythagoreantriple (p, q, r) is a triple of natural numbers p

The details are given in step 2.

Answered: 1 If n is a natural number and n ≥ 2,…

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1 If n is a natural number and n ≥ 2, then (2n, n²-1, n²+1) is a Pythagorean triple.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.4: Trigonometric Functions

Problem 76E

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Question

Either prove or disprove this mathematical claim detailed please

problems use Pythagorean Theorem, assumed to be true without any proof: "For
any right triangle, if its legs have length a and b and its hypotenuse length c, then a² + b²
c²." In
addition, two additional definitions are relevant to the conjectures you choose from below: a Pythagorean
triple (p, q, r) is a triple of natural numbers p <q <r such that p²+q² = r². An equilateral triangle is
one for which all three sides have equal length.
1 If n is a natural number and n ≥ 2, then (2n, n² − 1, n²+1) is a Pythagorean triple.

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