Question
The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.
✓
Answer
Let the numbers be x and y respectively.
According to the question:
$x - y = 14 ...(1)$
$x^2 - y^2 = 448 ...(2)$
From (1), we get:
$x = 14 + y ...(3)$
Putting x = 14 + y in (2), we get
$(14 + y)^2 - y^2 = 448$
$196 + y^2 + 28y - y^2 = 448$
$196 + 28y = 448$
$28y = 448 - 196$
$\text{y}=\frac{252}{28}$
y = 9
Putting y = 9 in (1), we get
x - 9 = 14
⇒ x = 14 + 9
⇒ x = 23
Hence, the required numbers are 23 and 9.
According to the question:
$x - y = 14 ...(1)$
$x^2 - y^2 = 448 ...(2)$
From (1), we get:
$x = 14 + y ...(3)$
Putting x = 14 + y in (2), we get
$(14 + y)^2 - y^2 = 448$
$196 + y^2 + 28y - y^2 = 448$
$196 + 28y = 448$
$28y = 448 - 196$
$\text{y}=\frac{252}{28}$
y = 9
Putting y = 9 in (1), we get
x - 9 = 14
⇒ x = 14 + 9
⇒ x = 23
Hence, the required numbers are 23 and 9.
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|
Class
|
5-15
|
15-25
|
25-35
|
35-45
|
45-55
|
55-65
|
65-75
|
|
Frequency
|
6
|
10
|
16
|
15
|
24
|
8
|
7
|