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UPSC CDS Math Linear Equations in One and Two Variables Questions
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© examsnet.com
Question : 1
Total: 41
If the sum of a real number and its reciprocal
26
5
is then how many such numbers are possible ?
[2019 CDS-II]
None
1
2
4
Validate
Solution:
We have a real number is
x
.
1
x
And, reciprocal of this number is
x
.
S
o
x
+
1
x
=
26
5
⇒
x
2
+
1
x
=
26
5
⇒
5
x
2
−
26
x
+
5
=
0
⇒
5
x
2
−
25
x
−
x
+
5
=
0
⇒
5
x
(
x
−
5
)
−
1
(
x
−
5
)
=
0
⇒
(
5
x
−
1
)
(
x
−
5
)
=
0
⇒
x
=
1
5
,
5
So, there are two types of such real numbers.
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