Write the Pythagorean triplet


Write the Pythagorean triplet whose one of the numbers is $4 .$


We know that, for any natural number greater than $1,\left(2 m, m^{2}-1, m^{2}+1\right)$ is a pythagorean triplet.

So, one number is $2 m$, then other two numbers are $m^{2}+1$ and $m^{2}-1$.

Hence, one number is 4 , then pythagorean triplet,

$2 m=4 \Rightarrow m=2$

$\therefore \quad m^{2}+1=2^{2}+1=4+1=5$

and $\quad m^{2}-1=2^{2}-1=4-1=3$

Now, $\quad 3^{2}+4^{2}=5^{2}$

$\Rightarrow \quad 9+16=25 \Rightarrow 25=25$

So, 3,4 and 5 are pythagorean triplets.


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