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Let x and y be real numbers satisfying 8/x=y/27=x/y Determine the value of x^3

 Jul 25, 2020
 #1
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Solution

The expression we want to find is .

Factor the given equations as  and , respectively. Dividing the latter by the former equation yields . Adding 3 to both sides and simplifying yields . Solving for  and substituting this expression into the first equation yields . Solving for , we find that , so . Substituting this into the second equation and solving for  yields . So, the expression to evaluate is equal to .        890

 Jul 25, 2020
 #2
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https://artofproblemsolving.com/wiki/index.php/2016_AIME_II_Problems/Problem_3

 Jul 25, 2020

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