Question

Question 10

Write the correct answer from the given four options.

If one member of a Pythagorean triplet is $2m$, then the other two members are

a) $m,m^2+1$
b) $m^2+1,m^2-1$
c) $m^2,m^2-1$
d) $m^2,m+1$

Answer 1

Option (b)
We know that, for any natural number m greater than 1, $(2m,m^2-1,m^2+1)$ is a Pythagorean triplet.
So, one number is 2m, then other two numbers are $m^2+1$ and $m^2-1$
Example: If one number is 4, then the pythagorean triplet
2m = 4
$\Rightarrow$ m = 2
$m^2+1=2^2+1=4+1=5$
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.