The product of two consecutive integers is 56. How do you find the integers?

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The product of two consecutive integers is 56. How do you find the integers?

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Answer 1 · 2016-06-02T12:04:52

The two numbers are 7 and 8.

Explanation:

$From the multiplications tables$ $color(blue)("From the multiplications tables")$

$7 \times 8 = 56$ $color(green)(7xx8=56)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$The algebra way$ $color(blue)("The algebra way")$
Let the first number be $n$ $n$

Then the second number is $n + 1$ $n+1$

The product is $n \times (n + 1) = 56$ $nxx(n+1) = 56$

$\Rightarrow n^{2} + n - 56 = 0$ $=>n^2+n-56=0$

Known: $7 \times 8 = 56$ $7xx8=56$ . However the equation's 56 is nagetive, so one of the 7 and 8 is negative.
The equation has $+ n$ $+n$ so the larger of the two is positive. Giving:

$(n - 7) (n + 8) = 0$ $(n-7)(n+8)=0$

$\Rightarrow n = + 7 and n = - 8$ $=> n = +7" and "n=-8$

As a first number $n = - 8$ $n=-8$ is not logical so the first number is $n = 7$ $n=7$

Thus the second number is 8.

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The product of two consecutive integers is 56. How do you find the integers?

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