document.write( "Question 1086799: If x^2 + 1/x^2 =102, find the value of x^3 - 1/x^3 \n" ); document.write( "
Algebra.Com's Answer #701042 by ikleyn(52788)\"\" \"About 
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document.write( "If \"x%5E2+%2B+1%2Fx%5E2\" = 102,  then  \"x%5E2\" - 2 + \"1%2Fx%5E2%29\" = 102 - 2 = 100, \r\n" );
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document.write( "or  \"%28x-1%2Fx%29%5E2\" = 100,  which implies   \"x+-+1%2Fx\" = 10  or  \"x-1%2Fx\" = -10.\r\n" );
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document.write( "If  \"x+-+1%2Fx\" = 10  then\r\n" );
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document.write( "    \"%28x+-+1%2Fx%29%5E3\" = 1000 = \"x%5E3+-+3x%5E2%2A%281%2Fx%29+%2B+3x%2A%281%2Fx%5E2%29+-+1%2Fx%5E3\" = \"%28x%5E3+-1%2Fx%5E3%29\" - \"%283x+-+3%2Fx%29\" = \"%28x%5E3+-+1%2Fx%5E3%29\" - \"3%2A%28x-1%2Fx%29\" = \"%28x%5E3+-+1%2Fx%5E3%29\" - 3*10.\r\n" );
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document.write( "It implies  \"%28x%5E3+-+1%2Fx%5E3%29\" = 1030.\r\n" );
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document.write( "If  \"x+-+1%2Fx\" = -10  then\r\n" );
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document.write( "    \"%28x+-+1%2Fx%29%5E3\" = -1000 = \"x%5E3+-+3x%5E2%2A%281%2Fx%29+%2B+3x%2A%281%2Fx%5E2%29+-+1%2Fx%5E3\" = \"%28x%5E3+-1%2Fx%5E3%29\" - \"3x+-+3%2Fx%29\" = \"%28x%5E3+-+1%2Fx%5E3%29\" - \"3%2A%28x-1%2Fx%29\" = \"%28x%5E3+-+1%2Fx%5E3%29\" - 3*(-10) = \"%28x%5E3+-+1%2Fx%5E3%29\" + 30.\r\n" );
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document.write( "It implies  \"%28x%5E3+-+1%2Fx%5E3%29\" = -1000 - 30 = -1030.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer.  Under the given condition,  the expression  \"%28x%5E3+-+1%2Fx%5E3%29\"  may have two values:  1030  or  -1030.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Two lessons to learn from this solution\r
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\n" ); document.write( "\n" ); document.write( "    1.  You do not need to solve equations to get the answer.\r
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\n" ); document.write( "\n" ); document.write( "    2.  The approach the tutor @rothauserc took to solve the problem is WRONG.\r
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