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Question

the difference between a positive fraction and its reciprocal is 9/20
find the sum of that fraction and its reciprocal.


Options:
A .  $$\cfrac{41}{20}$$
B .  $$\cfrac{17}{20}$$
C .  $$\cfrac{11}{20}$$
D .  $$\cfrac{9}{20}$$
Answer: Option A


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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