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

Answers (1)

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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