Question

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

Answer 1

Answer:

Let x and x+1 be the two consecutive positive integers .

Therefore, x (x+1) =306.

Or, x^2 +x -306 = 0.

Or, x^2 +(18-17)x - 306 = 0

Or, (x+18)(x-17) = 0

We get x =17,and -18.

so, the two consecutive positive integers are 17 and 18.

Answer 2

QUESTION :-

The product of two consecutive integers is 306 . we need to find the integers?

ANSWER :-

The product of two consecutive integer = 306

To Find -

Consecutive integer whose product is 306.

Now,

Let the two consecutive integers be (x) and (x+1).

$x(x + 1) = 306 \\ = > {x}^{2} + x \: = 306 \\ = > {x}^{2} + x - 306 = 0 \\ = > {x}^{2} + 18x - 17x - 306 = 0 \\ = > x(x + 18) - 17(x + 18) = 306 \\ = > (x + 18)(x - 17) = 0 \\ = > x + 18 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: x - 17 = 0 \\ = > x = - 18 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: and \: \: \: \: x \: = 17 \:$

Hence,

Case 1:- when x = 17

The first integer be 17.

& other be (x+1) = 17+1 = 18.

Case 2:- when x = - 18

The first integer be - 18

& other be (x+1) = - 18 +1 = - 17

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Thank you for the question !