document.write( "Question 763381: if (x+(1/x))=4 then find value of (x^3+(1/x^3)) \n" ); document.write( "

Algebra.Com's Answer #464779 by ramkikk66(644) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is very similar to question 763384, which has been solved.\r
\n" ); document.write( "\n" ); document.write( "We will use the identity \r
\n" ); document.write( "\n" ); document.write( " $\"%28a+%2B+b%29%5E3+=+a%5E3+%2B+b%5E3+%2B+3%2Aa%2Ab%28a+%2B+b%29\"$ ------- (1)\r
\n" ); document.write( "\n" ); document.write( " $\"x+%2B+1%2Fx+=+4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x+%2B+1%2Fx%29%5E3+=+4%5E3+=+64\"$ \r
\n" ); document.write( "\n" ); document.write( "But by the identity (1),\r
\n" ); document.write( "\n" ); document.write( " $\"%28x+%2B++1%2Fx%29%5E3+=+x%5E3+%2B+1%2Fx%5E3+%2B+3%2Ax%2A%281%2Fx%29%2A%28x+%2B+1%2Fx%29\"$ ------- (2)\r
\n" ); document.write( "\n" ); document.write( "Substituting for (x + 1/x) as 4\r
\n" ); document.write( "\n" ); document.write( " $\"%28x+%2B+1%2Fx%29%5E3+=+x%5E3+%2B+1%2Fx%5E3+%2B+3%2A1%2A4\"$ ------- (3) ---> x*1/x = 1\r
\n" ); document.write( "\n" ); document.write( " $\"64+=+x%5E3+%2B+1%2Fx%5E3+%2B+12\"$ ------ (4)\r
\n" ); document.write( "\n" ); document.write( "So, \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3+%2B+1%2Fx%5E3+=+64+-+12+=+52\"$ \r
\n" ); document.write( "\n" ); document.write( ":) \n" ); document.write( "

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