Question

Find the Pythagorean triplet whose one member is 37

Answer 1

As we know 2m, m 2 + 1 and m2 - 1 form a Pythagorean triplet for any number, m > 1.

Let's assume
M^2+1=37
Then, M^2=36
And M=6
Now put the value of M
2M = 12
M^2+1=37
M^2-1=35

The triplets are 37, 35 and 12

Answer 2

Answer:

The Pythagorean triplets are 12, 35 and 37.

Step-by-step explanation:

Given one member in Pythagorean triplet = 37

The measures of the form $2m$, $m^{2} + 1$ and $m^{2} - 1$ form a Pythagorean triplet for any number, m > 1.

If we take $2m=37$, it do not give you an integer.

If we take $m^{2} -1=37$, it do not form a perfect square.

So, let us take $m^{2} + 1=37$.

$\implies m^{2} =37-1=36$

$\implies m =\sqrt{36} =6$

Now substituting m in the general form of triplets,

$2m=2\times 6=12$

$m^{2} - 1=6^{2} -1=36-1=35$

and $m^{2} + 1=37$

Therefore, the Pythagorean triplets are 12, 35 and 37.