## Book: RS Aggarwal - Mathematics

### Chapter: 10. Quadratic Equations

#### Subject: Maths - Class 10th

##### Q. No. 3 of Exercise 10E

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

3
##### The sum of two natural numbers is 28 and their product is 192. Find the numbers.

Let the required number be x and 28 – x

According to given condition,

x(28 – x) = 192

x2 – 28x + 192 = 0

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 = 1 b = – 28 c = 192

= 1.192 = 192

And either of their sum or difference = b

= – 28

Thus the two terms are – 16 and – 12

Sum = – 16 – 12 = – 28

Product = – 16. – 12 = 192

x2 – 28x + 192 = 0

x2 – 16x – 12x + 192 = 0

x(x – 16) – 12(x – 16) = 0

(x – 16) (x – 12) = 0

(x – 16) = 0 or (x – 12) = 0

x = 16 or x = 12

Hence the required numbers are 16, 12

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