Question

For every natural number $m$, $\left(2m–1,2m^2–2m,2m^2–2m+1\right)$ is a Pythagorean triplet.

State whether the statement is true or false.

• A. True
• B. False

Answer 1

The correct option is B False

Define the Pythagorean triplet

1. According to the Pythagoras theorem, in a right angle triangle, ${\left(\mathrm{Hypotenus}\right)}^2={\left(\mathrm{Perpendicular}\right)}^2+{\left(\mathrm{Base}\right)}^2$
2. A group of three numbers, such that the sum of squares of two smaller numbers is equal to the square of the largest, is called a Pythagorean triplet.
3. For every natural number $m$, ${\left(2m\right)}^2+{\left(m^2-1\right)}^2={\left(m^2+1\right)}^2$

So, for any natural number $m$, the Pythagorean triplet is $\left(2m,m^2-1,m^2+1\right)$.

Hence, the given statement is false.