Question 10

Write the correct answer from the given four options.

If one member of a Pythagorean triplet is $2 m$ , 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) $m^{2}, m + 1$

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Solution

Option (b)
We know that, for any natural number m greater than 1, $(2 m, m^{2} - 1, m^{2} + 1)$ 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.

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Finding Pythagorean Triplets for Any Given Number

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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, m2+1 b) m2+1,m2−1 c) m2,m2−1 d) m2,m+1

Question 10

Write the correct answer from the given four options.

If one member of a Pythagorean triplet is $2 m$ , 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) $m^{2}, m + 1$