Question 1012448
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the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?
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Let x be that middle number.
Then the three numbers are (x-2), x, and (x+2).

Their product is P = (x-2)*x*(x+2) = x*(x^2 - 4).
Their sum is S = (x-2) + x + (x+2) = 3x.
The equation is 

{{{P/S}}} = 64,  or {{{(x*(x^2-4))/(3x)}}} = 64,  or  {{{(x^2-4)/3}}} = 64.


{{{x^2 - 4}}} = 64*3 = 192,  {{{x^2}}} = 192 + 4 = 196,  x = +/-14.

Since the condition talks about natural numbers, only positive value is the solution.

<U>Answer</U>. x = 14.
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