For every natural number m, (2m -1, 2m² -2m, 2m² -2m + 1) is a pythagorean triplet. State whether the statement is true or false.

Solution:

Given, For every natural number m, (2m -1, 2m² -2m, 2m² -2m + 1) is a pythagorean triplet.

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, the given statement is false.

✦ Try This: For every natural number m, (2m -1, 2m² + m, m² - m + 1) is a pythagorean triplet. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 65

For every natural number m, (2m -1, 2m² -2m, 2m² -2m + 1) is a pythagorean triplet. State whether the statement is true or false

Summary:

The given statement, ”For every natural number m, (2m -1, 2m² -2m, 2m² -2m + 1) is a pythagorean triplet” is false

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