Question 207364

The sum of two numbers is 34 and their product is 168. Find the two numbers. I don't understand what product means. Thank you.


SUM means ADD, while PRODUCT means MULTIPLY


Let the first number = F, and the second number = S


Then since their sum is 34, we get: F + S = 34 


Since their product is 168, then FS = 168 


F + S = 34 -----> F = 34 - S -----> equation (i)


FS = 168 ------> equation (ii)


Substitute 34 - S for F in eq (ii) -----> S(34 - S) = 168

{{{34S - S^2 = 168}}}

{{{S^2 - 34S + 168 = 0}}}


We're now looking for 2 factors whose products are + 168 (c * a), and whose sum is - 34. These 2 factors are (-28) and (-6).


Therefore, {{{S^2 - 34S + 168 = 0}}} -----> (S - 28)(S - 6) = 0


The smaller number is 6. Therefore, the two numbers are {{{highlight_green(6)}}} and {{{highlight_green(28)}}}