<PRE><B>Question 207613</B>

3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.


Let the smallest number be S


Then the other two numbers, since these are EVEN numbers are: S + 2, and S + 4


Now, since the product of the smaller two numbers is 52 less than the square of the largest number, we have: 

{{{S(S + 2) = (S + 4)^2 - 52)}}}

{{{S^2 + 2S = S^2 + 8S + 16 - 52}}}

2S - 8S = 16 - 52

- 6S  =  - 36

{{{S = (-36)/-6}}} = 6


Therefore, the smallest number is {{{highlight_green(6)}}}, the second smallest is {{{highlight_green(8)}}} (6 + 2), and the largest is {{{highlight_green(10)}}} (6 + 4) 


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Check:
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The product of the two smaller numbers, 6 and 8 is 48 (6 * 8)


The square of the largest number, 10, is 100 ({{{10^2}}})


48 (the product of the two smaller numbers) is 52 less than 100 (the square of the largest number) 


PLUS, the THREE are CONSECUTIVE EVEN NUMBERS


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