Stoockiltj5

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.

Bottisiooq

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

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

$x+1=8+19$
When x=-9
$x+1=-9+1-8$
Now,
$8×9=72$
$\left(-9\right)×\left(-8\right)=72$
The consecutive integers whose product is 72  or

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