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From the choices below, if one member of a pythagorean triplet is $2 m$ , then the other two members are:

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m, m 2 + 1

m 2 + 1, m 2 − 1

m 2, m 2 − 1

m 2, m + 1

answer is B.

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Detailed Solution

Given that one of the member of the pythagorean triplet is

2 m

.
We have to find the other two members.
As we know that, for every natural number

m

2 m, m 2 − 1, m 2 + 1

form a pythagorean triplet.
Consider an example.
We know that, (3, 4, 5) forms a pythagorean triplet.
Since

2 m, m^{2} - 1, m^{2} + 1

from a pythagorean triplet, put m = 2.
So, we get, 2m = 2(2)
= 4
=

m^{2} - 1 = 2^{2} - 1

= 4 - 1
= 3
And

m^{2} + 1 = 2^{2} + 1

= 4 + 1
= 5
And so, (3, 4, 5) forms a pythagorean triplet.
And hence,

2 m, m^{2} - 1, m^{2} + 1

forms pythagorean triplet.
The other two members are

m^{2} - 1, m^{2} + 1

.
Hence, option 2) is correct.

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