Question
Write the Pythagorean triplet whose one of the numbers is $4.$
✓
Answer
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 $2m$, then other two numbers are $m^2+1$ and $m^2-1$
Hence, one number is $4$, then pythagorean triplet,
$2m = 4 $
$\Rightarrow m = 2$
$\therefore m^2+1=2^2+1=4+1=5$
and $m^2-1=2^2-1=4-1=3$
Now, $3^2+4^2=5^2$
$\Rightarrow 9 + 16 = 25 $
$\Rightarrow 25 = 25$
So, $3, 4$ and $5$ are pythagorean triplets.
So, one number is $2m$, then other two numbers are $m^2+1$ and $m^2-1$
Hence, one number is $4$, then pythagorean triplet,
$2m = 4 $
$\Rightarrow m = 2$
$\therefore m^2+1=2^2+1=4+1=5$
and $m^2-1=2^2-1=4-1=3$
Now, $3^2+4^2=5^2$
$\Rightarrow 9 + 16 = 25 $
$\Rightarrow 25 = 25$
So, $3, 4$ and $5$ are pythagorean triplets.
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