## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 17 of Exercise 10E

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

17
##### The sum of a natural number and its reciprocal is 65/8. Find the number.

Let the required natural numbers x

According to given condition,

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 8 b = – 65 c = 8

= 8.8 = 64

And either of their sum or difference = b

= – 65

Thus the two terms are – 64 and – 1

Difference = – 64 – 1 = – 65

Product = – 64. – 1 = 64

8x (x – 8) – 1(x – 8) = 0

(x – 8) (8x – 1) = 0

(x – 8) = 0 or (8x – 1) = 0

x = 8 or x = 1/8

x = 8 (x is a natural number)

Hence the required number is 8.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71