Question

If two consecutive positive integers have the property that one integer times twice the other equals 612 what is the sum of these two integers?

Answer 1

If the smaller integer is `x`
we have either `(x) xx 2(x+1) = 612` or `2(x) xx (x+1) = 612`

in either case
`color(white)("XXXXX")` `2(x)(x+1) =612`

`color(white)("XXXXX")`2x^2+2x = 612#

`color(white)("XXXXX")`2x^2+2x-612 = 0#

Using the quadratic formula
`color(white)("XXXXX")` `x = (-2+-sqrt(4+4(2)(612)))/(2(2)`

`color(white)("XXXXX")` `=(-2+-sqrt(4900))/4`

`color(white)("XXXXX")` `=(-2+-70)/4`
(ignoring the negative value, since we are told the numbers are positive)
`color(white)("XXXXX")` `x=68/4 = 17`

and the two consecutive positive integers are 17 and 18