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Find two numbers whose sum is 27 and product is 182.
Given :
The product of the two numbers is 182 and their sum is 27.
To do :
We have to find the numbers.
Solution :
Let the numbers be $a$ and $b$.
Therefore,
$a + b = 27$
$b = 27-a$ -----(1)
$a \times b = 182$
$a \times (27-a) = 182$ [from (1)]
$a(27) - a(a) = 182$
$a^2-27a+182 = 0$
$a^2-13a-14a+182 = 0$
$a(a-13)-14(a-13) = 0$
$(a-13)(a-14)=0$
$a=13$ or $a=14$
If $a = 13$,
$b = 27-13 = 14$ [from (1)]
If $a = 14$,
$b = 27-14 = 13$ [from (1)]
The required numbers are 13 and 14.
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