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UPSC CDS Math Law of Indices Questions
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© examsnet.com
Question : 13
Total: 13
What are the possible solutions for x of the equation
x
√
x
=
n
√
x
x
where x and n are positive integers?
[2015 CDS-I]
0, n
1, n
n, n
1, n
Validate
Solution:
x
√
x
=
n
√
x
x
⇒
x
√
x
=
(
x
x
)
1
n
=
x
x
n
⇒
√
x
=
x
n
⇒
√
x
=
n
⇒
x
=
n
2
For
x
=
1
LHS
=
1
√
1
=
1
=
n
√
1
RHS
Thus, the possible solutions for the given equation are 1 and
n
2.
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