Question 306638
Please help me solve this. The product of two consecutive integers is equal to ten times the smaller integer minus eight. Find the integers.


Let the smaller integer be S


Then the larger consecutive integer is S + 1, and their product is S(S + 1)


Now, since their product is equal to ten times the smaller integer minus eight, then we'll have: S(S+ 1) = 10S - 8


{{{S^2 + S = 10S - 8}}}


{{{S^2 + S - 10S + 8 = 0}}}


{{{S^2 - 9S + 8 = 0}}}


(S - 8)(S - 1) = 0


Therefore, S, or the smaller integer = {{{8}}} or {{{1}}}, which means that the two consecutive integers are either {{{highlight_green(8)}}} and {{{highlight_green(9)}}} or {{{highlight_green(1)}}} and {{{highlight_green(2)}}}.