Question

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

Answer 1

The two numbers are 7 and 8.

Explanation:

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

`color(green)(7xx8=56)`

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

Then the second number is `n+1`

The product is `nxx(n+1) = 56`

`=>n^2+n-56=0`

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

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

`=> n = +7" and "n=-8`

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

Thus the second number is 8.