document.write( "Question 1105837: If x+(1/x) = -3, find the value of x-(1/x) \n" ); document.write( "
Algebra.Com's Answer #720732 by ikleyn(52855)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If  \"x\" + \"1%2Fx%29\" = -3,  then (square both sides) \r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E2\" = 9  ====>\r\n" );
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document.write( "\"x%5E2\" + \"2\" + \"1%2Fx%5E2\" = 9  ====>\r\n" );
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document.write( "\"x%5E2\" + \"1%2Fx%5E2\" = 9-2 = 7  ====>\r\n" );
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document.write( "\"x%5E2\" - \"2\" + \"1%2Fx%5E2\" = 7 - 2 = 5  ====>\r\n" );
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document.write( "\"%28x-1%2Fx%29%5E2\" = 5  ====>  \"x\" - \"1%2Fx\" = +/- \"sqrt%285%29\".\r\n" );
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document.write( "And both values  \"sqrt%285%29\" and \"-sqrt%285%29\" are achievable.\r\n" );
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document.write( "If  \"x\" + \"1%2Fx%29\" = -3,  then \r\n" );
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document.write( "\"x%5E2+%2B+3x+%2B+1\" = 0  ====>\r\n" );
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document.write( "\"x%5B1%2C2%5D\" = \"%28-3+%2B-+sqrt%289-4%29%29%2F2\" = \"%28-3+%2B-+sqrt%285%29%29%2F2\".\r\n" );
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document.write( "1.  If  x = \"%28-3+%2B+sqrt%285%29%29%2F2\",  then\r\n" );
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document.write( "    \"1%2Fx\" = \"1%2F%28-3+%2B+sqrt%285%29%29%2F2\" = \"2%2F%28-3+%2B+sqrt%285%29%29\" = \"2%2A%28-3-sqrt%285%29%29%2F%289-5%29\" = \"%28-3%2Bsqrt%285%29%29%2F2\".\r\n" );
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document.write( "    Then  \"x\" - \"1%2Fx\" = \"%28-3+%2B+sqrt%285%29%29%2F2\" - \"%28-3+-+sqrt%285%29%29%2F2\" = \"sqrt%285%29\".\r\n" );
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document.write( "2.  If  x = \"%28-3+-+sqrt%285%29%29%2F2\",  then similarly\r\n" );
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document.write( "    \"1%2Fx\" = \"1%2F%28-3+-+sqrt%285%29%29%2F2\" = \"2%2F%28-3+-+sqrt%285%29%29\" = \"2%2A%28-3%2Bsqrt%285%29%29%2F%289-5%29\" = \"%28-3%2Bsqrt%285%29%29%2F2\".\r\n" );
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document.write( "    Then  \"x\" - \"1%2Fx\" = \"%28-3+-+sqrt%285%29%29%2F2\" - \"%28-3+%2B+sqrt%285%29%29%2F2\" = \"-sqrt%285%29\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (two times with the identical answers !).
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\n" ); document.write( "\n" ); document.write( "The answer by @josgarithmetic is   I N C O R R E C T.\r
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\n" ); document.write( "For many similar solved problems see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate expressions involving  \"%28x+%2B+1%2Fx%29\",  \"%28x%5E2%2B1%2Fx%5E2%29\",  \"%28x%5E3+%2B+1%2Fx%5E3%29\"  and  \"%28x%5E5%2B1%2Fx%5E5%29\"\r
\n" ); document.write( "\n" ); document.write( "    - Advanced lesson on evaluating expressions\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a quadratic equation\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Evaluation, substitution\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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