Question 634305

Given three consecutive odd numbers such that the square of the second number is 192 less than the square of the third. Find those numbers.


Let the 1st of the integers be F


Then 2nd and 3rd are F + 2, and F + 4, respectively


Based on the given info, we see that: {{{(F + 2)^2 = (F + 4)^2 - 192}}}


{{{F^2 + 4F + 4 = F^2 + 8F + 16 - 192}}}


{{{F^2 - F^2 + 4F - 8F = - 176 - 4}}}


- 4F = - 180


F, or 1st integer = {{{(- 180)/- 4}}}, or {{{45}}}


Therefore, the three consecutive odd integers are: {{{highlight_green(45_47_and_49)}}}


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