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+28 y-y^2=448 $
$ 196+28 y=448 $
$ 28 y=448-196 $
$ 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+28 y-y^2=448 $
$ 196+28 y=448 $
$ 28 y=448-196 $
$ 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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