Explained: "The product of two consecutive integers is 72...."

High School
Algebra
Algebra I
Quadratic function and equation

Stoockiltj5

Answered question

2022-01-31

The product of two consecutive integers is 72. Find the two pairs of integers.
we are dealing with quadratics and i am not sure how to set this up into solvable equation.

Answer & Explanation

Bottisiooq

Beginner2022-02-01Added 9 answers

Let x be the first integer. The second integer will be x+1 because the two integers are consecutive,
x(x+1)=72
$x^{2} = x = 72$
$x^{2} = x - 72 = 0$
$x = \frac{- 1 \pm \sqrt{1^{2} - 4.1 . (- 72)}}{2.1}$
$x = \frac{- 1 \pm \sqrt{1 + 288}}{2}$
$x = \frac{- 1 \pm \sqrt{1 + 289}}{2}$
$= \frac{- 1 \pm 17}{2}$
$= \frac{16}{2}, - \frac{18}{2}$

$= 8, - 9$
When x=8,

$x + 1 = 8 + 19$
When x=-9
$x + 1 = - 9 + 1 - 8$
Now,
$8 \times 9 = 72$
$(- 9) \times (- 8) = 72$
The consecutive integers whose product is 72 $b f a r e 8 and 9$ or $b f - 9 and - 8 .$

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