Question

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

Answer 1

Step-by-step explanation:

Let one consecutive positive interger be = x

So, second consecutive interger=x+1

ACCORDING TO QUESTION

Product of these conecutive integers is 306

= x(x+1)=306

= x² + x -306=0

=BY MIDDLE TERM SPLIT METHOD

= x² +18x - 17x -306

= x (x + 18) -17(x +18)

= (x - 17) (x + 18)

= x - 17 = 0 ; x = 17

= x + 18 = 0 ; x = -18

We take x = 17 because consecutive numbers are not in negative.

Therefore , one consecutive integer is = 17

and another consecutive integer is = x + 1

17 + 1 = 18

HOPES THIS HELPS YOU..........

Answer 2

$\huge\mathrm{Solution}$

Let the first integer be x.

Second integer = x+1

Product of two integers=306

$x(x + 1) = 306 \\ {x}^{2} + x = 306 \\ {x}^{2} + x - 306 = 0$

Splitting the middle term-

${x}^{2} + x - 306 = 0 \\ {x}^{2} + (18 - 17)x - 306 = 0 \\ {x}^{2} + 18x - 17x - 306 = 0 \\ x(x + 18) - 17(x + 18) = 0 \\ (x - 17)(x + 18) = 0$

So,

$x = 17 \\ x = - 18$

So,The first integer is 17.

And the second integer is 18.