document.write( "Question 1151183: Evaluate sqrt(y/x), where x and y are positive integers, and 0 = x^5-(x^3)(y^3)-12393. \n" ); document.write( "

Algebra.Com's Answer #772827 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"0+=+x%5E5-%28x%5E3%29%28y%5E3%29-12393\"$

\n" ); document.write( "Rewrite the equation as

\n" ); document.write( " $\"x%5E3%28x%5E2-y%5E3%29+=+12393\"$

\n" ); document.write( "Then find the prime factorization of 12393:

\n" ); document.write( " $\"12393+=+%283%5E6%29%2817%29\"$

\n" ); document.write( "So

\n" ); document.write( " $\"%28x%5E3%29%28x%5E2-y%5E3%29+=+%283%5E6%29%2817%29\"$

\n" ); document.write( "Since x and y are positive integers,
\n" ); document.write( " $\"x%5E3=+3%5E6\"$
\n" ); document.write( "means either $\"x=3\"$ or $\"x=3%5E2=9\"$ .

\n" ); document.write( "If x=3,
\n" ); document.write( " $\"%28x%5E3%29%28x%5E2-y%5E3%29+=+%2827%29%289-y%5E3%29+=+12393\"$
\n" ); document.write( "which is clearly not possible.

\n" ); document.write( "If x=9,
\n" ); document.write( " $\"%28x%5E3%29%28x%5E2-y%5E3%29+=+%28729%29%2881-y%5E3%29+=+729%2A17\"$
\n" ); document.write( " $\"81-y%5E3=17\"$
\n" ); document.write( " $\"y%5E3=64\"$
\n" ); document.write( " $\"y=4\"$

\n" ); document.write( "So x=9 and y=4; and then

\n" ); document.write( "ANSWER: $\"sqrt%28y%2Fx%29+=+sqrt%284%2F9%29+=+2%2F3\"$

\n" ); document.write( " \n" ); document.write( "

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