document.write( "Question 762576: $\"x=%283+%2B+sqrt+%28+5+%29%29%2F%283+-+sqrt+%28+5+%29%29\"$ and $\"y+=%283+-+sqrt+%28+5+%29%29%2F%283+%2B+sqrt+%28+5+%29%29\"$ . calculate $\"x%5E3+%2B+y%5E3\"$ \n" ); document.write( "

Algebra.Com's Answer #464076 by DrBeeee(684) $\"\"$ $\"About$

You can put this solution on YOUR website!
This a lot of multiplying, but here goes. Start with
\n" ); document.write( "(1) $\"x+=+%283+%2B+sqrt%285%29%29%2F%283+-+sqrt%285%29%29\"$
\n" ); document.write( "Now multiply numerator and denominator of (1) by
\n" ); document.write( "(2) $\"%283+%2B+sqrt%285%29%29\"$ and get
\n" ); document.write( "(3) $\"x+=+%289+%2B+6sqrt%285%29+%2B5%29%2F4\"$ or
\n" ); document.write( "(4) $\"x+=+%2814+%2B+6sqrt%285%29%29%2F4\"$ or
\n" ); document.write( "(5) $\"x+=+%287+%2B+3sqrt%285%29%29%2F2\"$
\n" ); document.write( "Now get
\n" ); document.write( "(6) $\"x%5E2+=+%2849%2B42sqrt%285%29%2B45%29%2F4\"$ or
\n" ); document.write( "(7) $\"x%5E2+=+%2894%2B42sqrt%285%29%29%2F4\"$
\n" ); document.write( "Now get $\"x%5E3\"$ from
\n" ); document.write( "(8) $\"x%5E3+=+x%2Ax%5E2\"$ or
\n" ); document.write( "(9) $\"x%5E3+=+%287+%2B+3sqrt%285%29%29%2A%2894%2B42sqrt%285%29%29%2F8\"$ or
\n" ); document.write( "(10) $\"x%5E3+=+%287%2A94+%2B+%283%2A94+%2B+7%2A42%29%2A%28sqrt%285%29%29%2B+3%2A42%2A5%29%2F8\"$ or
\n" ); document.write( "(11) $\"x%5E3+=+%28658+%2B+576%28sqrt%285%29%29%2B+630%29%2F8\"$ or
\n" ); document.write( "(12) $\"x%5E3+=+161+%2B+72sqrt%285%29\"$
\n" ); document.write( "From the original problem we see that
\n" ); document.write( "(13) y = 1/x or
\n" ); document.write( "(14) $\"y%5E3+=+1%2Fx%5E3\"$ or
\n" ); document.write( "(15) $\"y%5E3+=+1%2F%28161%2B72sqrt%285%29%29\"$
\n" ); document.write( "Now add (12) and (15) to get the desired sum
\n" ); document.write( "(16) $\"x%5E3%2By%5E3=+161+%2B+72sqrt%285%29+%2B++1%2F%28161%2B72sqrt%285%29%29\"$ or
\n" ); document.write( "(17)

or
\n" ); document.write( "(18) $\"x%5E3%2By%5E3=+%2851842+%2B+23184sqrt%285%29%29%2F%28161%2B72sqrt%285%29%29\"$
\n" ); document.write( "The GCF of the numerator of (18) is 2*7*23 or 322. So we can write (18) as
\n" ); document.write( "(19) $\"x%5E3%2By%5E3=+322%2A%28161+%2B+72sqrt%285%29%29%2F%28161%2B72sqrt%285%29%29\"$ which reduces to
\n" ); document.write( "the final answer,
\n" ); document.write( "(20) $\"x%5E3%2By%5E3=+322\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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