Question

the product of two consecutive positive integer is 306 we need to find the integers

Answer 1

The integers are....
1 ) 17......
2 ) 18....

Let integers are x , X+1

( x) (x+1) = 306.
x^2 + x - 306 = 0
x^2 + 18 x - 17 x -306. = 0
x ( x + 18 ) -17 ( x + 18 ) = 0
( x + 18 ). ( x -17 )
X = -18 , 17

as integers are positive therefore , negelecting -18...
The integers are ....
X = 17
X + 1 = 18 ...

Hope it helps to you.....
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Answer 2

Let us consider,

The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

Product of two consecutive integers = x × (x +1) = 306

⇒ x2 + x = 306

⇒ x2 + x – 306 = 0

Therefore, the two integers x and x+1, satisfies the quadratic equation, x2 + x – 306 = 0, which is the required representation of the problem mathematically.