Question 490009
the difference of two numbers is 3 and the product is 10. what are the two numbers?


Let the first number be F, and the second S


We can therefore say that: 


F - S = 3 ------ S = F - 3 ------ eq (i)
FS = 10 ------ eq (ii)


F(F - 3) = 10 ------ Substituting F - 3 for S in eq (ii) 


{{{F^2 - 3F - 10 =0 }}}


(F - 5)(F + 2) = 0


F - 5 = 0, or F + 2 = 0


F, or first number = 5 or - 2


Substituting 5 for F in eq (ii), we find that S, or second number = 2

Substituting - 2 for F in eq (ii), we find that S, or second number =  - 5
 

This means that the numbers are either: {{{highlight_green(5_and_2)}}} or {{{highlight_green(- 2_and_- 5)}}}


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