document.write( "Question 763384: if (x-(1/x))=3 find the value of (x^3-(1/x^3)) \n" ); document.write( "

Algebra.Com's Answer #464776 by ramkikk66(644) $\"\"$ $\"About$

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We will use the identity \r
\n" ); document.write( "\n" ); document.write( " $\"%28a+-+b%29%5E3+=+a%5E3+-+b%5E3+-+3%2Aa%2Ab%28a+-+b%29\"$ ------- (1)\r
\n" ); document.write( "\n" ); document.write( " $\"x+-+1%2Fx+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x+-+1%2Fx%29%5E3+=+3%5E3+=+27\"$ \r
\n" ); document.write( "\n" ); document.write( "But by the identity (1),\r
\n" ); document.write( "\n" ); document.write( " $\"%28x+-+1%2Fx%29%5E3+=+x%5E3+-+1%2Fx%5E3+-+3%2Ax%2A%281%2Fx%29%2A%28x+-+1%2Fx%29\"$ ------- (2)\r
\n" ); document.write( "\n" ); document.write( "Substituting for (x - 1/x) as 3\r
\n" ); document.write( "\n" ); document.write( " $\"%28x+-+1%2Fx%29%5E3+=+x%5E3+-+1%2Fx%5E3+-+3%2A1%2A3\"$ ------- (3) ---> x*1/x = 1\r
\n" ); document.write( "\n" ); document.write( " $\"27+=+x%5E3+-+1%2Fx%5E3+-+9\"$ ------ (4)\r
\n" ); document.write( "\n" ); document.write( "So, \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3+-+1%2Fx%5E3+=+36\"$ \r
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