Question
the difference between a positive fraction and its reciprocal is 9/20
find the sum of that fraction and its reciprocal.
Answer: Option A
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Then
x
−
1
x
=
9
20
⇒
x
2
−
1
x
=
9
20
⇒
x
2
−
1
=
9
x
20
⇒
20
x
2
−
20
=
9
x
⇒
20
x
2
−
9
x
−
20
=
0
x
=
−
b
±
b
2
−
4
a
c
2
a
=
9
±
−
9
2
−
4
×
20
×
−
20
2
×
20
=
9
±
81
+
1600
40
=
9
±
41
40
=
50
40
Or
−
32
40
Given that the fraction is positive. Hence
x
=
50
40
=
5
4
1
x
=
4
5
x
+
1
x
=
5
4
+
4
5
=
5
×
5
+
4
×
4
20
=
41
20
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