Question

product of 2 consecutive positive integers are 306 find integer

Answer 1

1st number= x
2nd number = x+2
so x(x+2)= 306
x² + 2x -306=0
by making the factors we will get
x-17= 0, x=17
x +18=0, x=-18

so clearly x=17 and x +1=18

Answer 2

let first integer be x 
then second will be x+1 
according to the given equation- 
x into (x+1) = 306
solving it, 
x² +x = 306
x² +x - 306 = 0
splitting the middle term, we get
x² + 18x -17x -306 = 0
x (x+18) - 17(x+18) = 0
(x+18) (x-17) = 0 
x= -18 or x = 17 
it cant be negative , so we take it as 17 and thus the other no. will be 18