Question 125012
Consecutive odd integers follow the pattern {{{2x+1}}}, {{{2x+3}}}, {{{2x+5}}}, etc





Since the product of two consecutive odd integers is 255, this means we have the equation


{{{(2x+1)(2x+3)=255}}}



{{{4x^2+8x+3=255}}} Foil the left side



{{{4x^2+8x-252}}} Subtract 255 from both sides



{{{4(x+9)(x-7)=0}}} Factor the left side 




Now set each factor equal to zero:

{{{x+9=0}}} or  {{{x-7=0}}} 


{{{x=-9}}} or  {{{x=7}}}    Now solve for x in each case



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Let's use the first solution {{{x=-9}}} to find the first pair of numbers


Now plug in {{{x=-9}}} into the first equation {{{2x+1}}}


{{{2(-9)+1=-18+1=-17}}}


Now plug in {{{x=-9}}} into the second equation {{{2x+3}}}


{{{2(-9)+3=-18+3=-15}}}



So the first pair of numbers are -17 and -15


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Let's use the second solution {{{x=7}}} to find the second pair of numbers


Now plug in {{{x=7}}} into the first equation {{{2x+1}}}


{{{2(7)+1=14+1=15}}}


Now plug in {{{x=7}}} into the second equation {{{2x+3}}}


{{{2(7)+3=14+3=17}}}



So the second pair of numbers are 15 and 17





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Answer: 



So the pair of consecutive odd integers that multiply to 255 are


-17 and -15


OR



15 and 17