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Question

The product of two consecutive positive integer is 306. Find the interger
 


Solution

Let one integer  be x then next will be x+1 
their product= x(x+1) 
According to question 
x(x+1) =306 
x^2+ x -306 =0 
two  number such that their sum is 1 and product is -306 are 
18-17 = 1
18x-17 = -306
x^2+18x-17x-306=0 
x(x+18) -17(x+18) =0 
(x-17) (x+18) =0 
x =17 and x=-18 
since number has to be positive (according to question) 
so x =17 
another number is 17+1 = 18 

 

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