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
$x - 9 = 14$
$\Rightarrow x = 14 + 9$
$\Rightarrow x = 23$
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
$x - 9 = 14$
$\Rightarrow x = 14 + 9$
$\Rightarrow x = 23$
Hence, the required numbers are $23$ and $9.$
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