All numbers of a pythagorean triplet are odd. State whether the statement is true or false.

Solution:

Given, all numbers of a pythagorean triplet are odd.

We have to determine if the given statement is true or false.

Pythagorean triples formula is used to find the triples or group of three terms that satisfy the pythagorean theorem.

For every natural number m > 1, 2m, m² - 1 and m² + 1 form a pythagorean triplet.

Other two members are m² - 1 and m² + 1

Example: Consider 2m = 4

m = 4/2

m = 2

So, m²-1 = (2)² - 1

= 4 - 1

= 3

So, m²+1 = (2)² + 1

= 4 + 1

= 5

The pythagorean triplet is 3, 4, 5.

Therefore, all numbers of a pythagorean triplet are not odd.

✦ Try This: All numbers of a pythagorean triplet are even. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 66

All numbers of a pythagorean triplet are odd. State whether the statement is true or false

Summary:

The given statement, ”All numbers of a pythagorean triplet are odd” is false.

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