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The sum of two numbers is 48 and their product is 432. Find the numbers.
Given:
The sum of two numbers is 48 and their product is 432.
To do:
We have to find the numbers.
Solution:
Let one of the numbers be $x$.
This implies,
The other number $=48-x$.
According to the question,
$x(48-x)=432$
$48x-x^2=432$
$x^2-48x+432=0$
Solving for $x$ by factorization method, we get,
$x^2-36x-12x+432=0$
$x(x-36)-12(x-36)=0$
$(x-36)(x-12)=0$
$x-36=0$ or $x-12=0$
$x=36$ or $x=12$
Therefore, the two numbers are $12$ and $36$.
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