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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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