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Q.

The two numbers whose sum is 27 and product is 182 are ____.


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Detailed Solution

Let the two numbers be x and y. Given that the sum is 27 and the product is 182.
We have,
x+y=27  
y=27−x   … (1)
xy=182   … (2)
Substitute (1) in (2), and we have
x(27−x)=182 27x− x 2 =182 x 2 −27x+182=0 x 2 −14x−13x+182=0 x(x−14)−13(x−14)=0 (x−14)(x−13)=0  
We have,
x−14=0 x=14   (or) x−13=0 x=13  
Substitute the above values in the equation (1), and we have
y=27−14 =13 y=27−13 =14  
Hence, the two numbers are (14,13)   and (13,14)  .
 
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