Question

The product of two consecutive positive integer is 306​

Answer 1

Answer:

$\Large \boxed{\sf 17 \ and \ 18}$

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

$(x) \times (x+1) =306$

Solve for x.

Expand brackets.

$x^2 +x =306$

Subtract 306 from both sides.

$x^2 +x -306=306-306$

$x^2 +x -306=0$

Factor left side of the equation.

$(x-17)(x+18)=0$

Set factors equal to 0.

$x-17=0$

$x=17$

$x+18=0$

$x=-18$

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

$(17)+1$

$18$

The two integers are 17 and 18.

Answer 2

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

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