Question 1189174
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The difference between two years from now and two years ago is 4 years.  Since the ages two years from now are perfect cubes and the ages two years ago are perfect squares, what you need to find is perfect cubes that are 4 greater than a perfect square.<br>
So look at perfect cubes, subtract 4, and see if the square root of the result is an integer.<br><pre>
   n  n^3  n^3-4  sqrt(n^3-4)
  ---------------------------
   1    1     -3     ---
   2    8      4      2
   3   27     23      x
   4   64     60      x
   5  125    121     11</pre>
That gives us the ages of the two trees as 6 and 123.<br>
ANSWER: The sum of the ages of the two oak trees is 6+123=129 years.<br>
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HELPFUL NOTE: Similar problems can be solved using an excel file or a graphing calculator.  On the spreadsheet or the graphing calculator, define a function as<br>
{{{sqrt(x^3-4)}}}<br>
and look for integer values of the function<br>