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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 62
Total: 68
Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units ?
where n is a positive real number.
[2014 CDS-I]
(
2
n
+
1
,
4
n
,
2
n
2
+
2
n
)
(
2
n
,
4
n
,
n
2
+
1
)
(
2
n
2
,
2
n
,
2
n
+
1
)
(
2
n
,
n
2
−
1
,
n
2
+
1
)
Validate
Solution:
None of the sides given in the options (a), (b) and (c) differs by two.
Consider the sides given in option (d).
Here,
(
n
2
+
1
)
2
=
n
4
+
2
n
2
+
1
=
(
n
2
−
1
)
2
+
(
2
n
)
2
so,
(
2
n
,
n
2
−
1
,
n
2
+
1
)
forms a Pythagorean triplet.
Also,
A
C
−
B
C
=
(
n
2
+
1
)
−
(
n
2
−
1
)
=
2
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