document.write( "Question 1046945: Kindly help me solving it i tried my best but I couldn't
\n" ); document.write( "Solving equation (x-1/x)^2-6 (x+1/x)+12=0 we get roots as?
\n" ); document.write( "I tried to simplify it and it reduced to
\n" ); document.write( "x^4-6x^3+14x^2-6x+1=0
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Algebra.Com's Answer #662401 by ikleyn(52864)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Kindly help me solving it i tried my best but I couldn't
\n" ); document.write( "Solving equation (x-1/x)^2-6 (x+1/x)+12=0 we get roots as?
\n" ); document.write( "I tried to simplify it and it reduced to
\n" ); document.write( "x^4-6x^3+14x^2-6x+1=0
\n" ); document.write( "But i can't go further
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document.write( "It is elementary . . . \r\n" );
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document.write( "0.  \"%28x-1%2Fx%29%5E2-6+%28x%2B1%2Fx%29%2B12\" = 0.    (1)\r\n" );
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document.write( "1.  \"%28x-1%2Fx%29%5E2\" = \"x%5E2+-2\" + \"1%2Fx%5E2\" = \"x%5E2+%2B+2\" + \"1%2Fx%5E2\" -4 = \"%28x%2B1%2Fx%29%5E2\" - 4.\r\n" );
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document.write( "2.  Therefore, you can write the original equation in an equivalent form\r\n" );
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document.write( "    \"%28x%2B1%2Fx%29%5E2+-+4+-+6%28x+%2B+1%2Fx%29+%2B+12\" = 0,  or, which is the same\r\n" );
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document.write( "    \"%28x%2B1%2Fx%29%5E2+-+6%28x+%2B+1%2Fx%29+%2B+8\" = 0.     (2)\r\n" );
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document.write( "3.  Next, introduce new variable y = \"x+%2B+1%2Fx\". Then the equation (2) takes the form\r\n" );
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document.write( "    \"y%5E2+-6y+%2B8\" = 0,\r\n" );
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document.write( "    and you can solve it by factoring\r\n" );
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document.write( "    ((y-4)*(y-2) = 0.\r\n" );
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document.write( "    The roots are y=4  and  y=2.\r\n" );
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document.write( "4.  As the last, final step, you should solve these two separate equations     \r\n" );
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document.write( "       \"x+%2B+1%2Fx\" = 6,\r\n" );
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document.write( "    and\r\n" );
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document.write( "       \"x+%2B+1%2Fx\" = 2.\r\n" );
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