# Q3.    Find two numbers whose sum is 27 and product is 182.

Let two numbers be x and y.

Then, their sum will be equal to 27 and the product equals 182.

$x+y = 27$                                        ...............................(1)

$xy =182$                                           .................................(2)

From equation (2) we have:

$y = \frac{182}{x}$

Then putting the value of y in equation (1), we get

$x+\frac{182}{x} = 27$

Solving this equation:

$\Rightarrow x^2-27x+182 = 0$

$\Rightarrow x^2-13x-14x+182 = 0$

$\Rightarrow x(x-13)-14(x-13) = 0$

$\Rightarrow (x-14)(x-13) = 0$

$\Rightarrow x = 13\ or\ 14$

Hence, the two required numbers are $13\ and \ 14$.

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