In this lesson, we are going to learn about the Pythagorean triplets.
A triplet \(a, b, c\) of three natural numbers \(a\), \(b\), and \(c\) is called a Pythagorean triplets, if .
I) \((3, 4, 5)\)
II) \((15, 8, 17)\)
To find a Pythagorean triplet:
We can write the Pythagorean triplet using this formula .
Here is Pythagorean triplet for any natural number .
Note: If \(a\) and \(b\) are relatively prime natural numbers such that and exactly one of them is even and other is odd, and the three numbers contain no common factors.
For example: Find a Pythagorean triplet whose one number is 14.
We know that is a Pythagorean triplet.
Now equate the given number with \(2a\) to find the value of \(a\).
Now substitute the \(a\) in the known formula , then we get,
Therefore the Pythagorean triplets are \((14, 48, 50)\).