document.write( "Question 877681: 12(x^2+1/x^2)-56(x+1/x)+89=0\r
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Algebra.Com's Answer #529518 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\"12%28x%5E2%2B1%2Fx%5E2%29-56%28x%2B1%2Fx%29%2B89\"\"%22%22=%22%22\"\"%220%22\"
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document.write( "Let \"u\"\"%22%22=%22%22\"\"x%2B1%2Fx\"\r\n" );
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document.write( "Then\r\n" );
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document.write( "    \"u%5E2\"\"%22%22=%22%22\"\"%28x%2B1%2Fx%29%5E2\"\"%22%22=%22%22\"\"x%5E2%2B2%2B1%2Fx%5E2\"\r\n" );
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document.write( "    \"u%5E2\"\"%22%22=%22%22\"\"x%5E2%2B1%2Fx%5E2%2B2\"\r\n" );
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document.write( "    \"u%5E2-2\"\"%22%22=%22%22\"\"x%5E2%2B1%2Fx\"\r\n" );
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document.write( "So substitute \"u%5E2-2\" for \"x%5E2%2B1%2Fx\"\r\n" );
document.write( "and \"u\" for \"x%2B1%2Fx\"\r\n" );
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document.write( "\"12%28u%5E2-2%29-56u%2B89\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "\"12u%5E2-24-56u%2B89\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "\"12u%5E2-56u%2B65\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "\"%286u-13%29%282u-5%29\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "6u - 13 = 0;       2u - 5 = 0\r\n" );
document.write( "     6u = 13           2u = 5\r\n" );
document.write( "      u = \"13%2F6\"         u =\"5%2F2\"\r\n" );
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document.write( "For u = \"13%2F6\", since \"u\"\"%22%22=%22%22\"\"x%2B1%2Fx\"\r\n" );
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document.write( "\"x%2B1%2Fx\"\"%22%22=%22%22\"\"13%2F6\"\r\n" );
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document.write( "Multiply through by 6x\r\n" );
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document.write( "\"6x%5E2%2B6\"\"%22%22=%22%22\"\"13x\"\r\n" );
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document.write( "\"6x%5E2-13x%2B6\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "(3x-2)(2x-3) = 0\r\n" );
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document.write( "3x-2 = 0;     2x-3 = 0\r\n" );
document.write( "  3x = 2;       2x = 3 \r\n" );
document.write( "   x = \"2%2F3\";       x = \"3%2F2\"\r\n" );
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document.write( "------\r\n" );
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document.write( "For u = \"5%2F2\", since \"u\"\"%22%22=%22%22\"\"x%2B1%2Fx\"\r\n" );
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document.write( "\"x%2B1%2Fx\"\"%22%22=%22%22\"\"5%2F2\"\r\n" );
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document.write( "Multiply through by 2x\r\n" );
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document.write( "\"2x%5E2%2B2\"\"%22%22=%22%22\"\"5x\"\r\n" );
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document.write( "\"2x%5E2-5x%2B2\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "(2x-1)(x-2) = 0\r\n" );
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document.write( "2x-1 = 0;      x-2 = 0\r\n" );
document.write( "  2x = 1;        x = 2 \r\n" );
document.write( "   x = \"1%2F2\";       \r\n" );
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document.write( "So there are four solutions:\r\n" );
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document.write( "x = \"2%2F3\"\r\n" );
document.write( "x = \"3%2F2\"\r\n" );
document.write( "x = \"1%2F2\"\r\n" );
document.write( "x = 2\r\n" );
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document.write( "Edwin

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