Question 1160416
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{{{(a^3 - b^3)/(a-b)^3= 73/3}}}<br>
{{{((a-b)(a^2+ab+b^2))/(a-b)^3 = 73/3}}}<br>
{{{(a^2+ab+b^2)/(a^2-2ab+b^2) = 73/3}}}<br>
{{{73a^2-146ab+73b^2 = 3a^2+3ab+3b^2}}}<br>
{{{70a^2-149ab+70b^2 = 0}}}<br>
{{{(7a-10b)(10a-7b) = 0}}}<br>
{{{7a = 10b}}}  or  {{{10a = 7b}}}<br>
Then, since a and b are relatively prime integers with a > b > 0, a = 10 and b = 7.<br>
And so a-b = 3.<br>
ANSWER: a-b = 3<br>