document.write( "Question 1042993: x=3+root8, then (x^6+x^4+x^2+1)/x^3\r
\n" ); document.write( "\n" ); document.write( "ans:204
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\n" ); document.write( "we have to solve this in 2 minutes \n" ); document.write( "

Algebra.Com's Answer #658157 by ikleyn(52852) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "x=3+root8, then (x^6+x^4+x^2+1)/x^3\r
\n" ); document.write( "\n" ); document.write( "ans:204
\n" ); document.write( "shortcut formula as possible
\n" ); document.write( "we have to solve this in 2 minutes
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document.write( "1.  Let us consider these two numbers: x =  and y = .\r\n" );
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document.write( "    It is easy to check that x*y =  =  = 9 - 8 = 1.    (1)\r\n" );
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document.write( "    Thus  y = ;  x  and  y are reciprocal.\r\n" );
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document.write( "    Also notice that  =  =  = 6.                      (2)\r\n" );
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document.write( "    Also notice that  =  =  = 36,\r\n" );
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document.write( "         therefore  = 36 - 2 = 34.                                      (3)\r\n" );
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document.write( "    Armed with this knowldge, we can make the next step.\r\n" );
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document.write( "2.  Let us regroup\r\n" );
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document.write( "       =  +  =  +  = \r\n" );
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document.write( "    =  +  =     ( now substitute x + y = 6, according to (2) )\r\n" );
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document.write( "    =  +  =  = 6*34 = 204.   ( I substituted   +  = 34, according to (3) )\r\n" );
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document.write( "Answer.   = 204.\r\n" );
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\n" ); document.write( "Are you shocked?\r
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\n" ); document.write( "\n" ); document.write( "I think it would be normal reaction for an unprepared person to be chocked.\r
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\n" ); document.write( "\n" ); document.write( "But I am prepared.\r
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\n" ); document.write( "\n" ); document.write( "And I can help you to get to be prepared too.\r
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\n" ); document.write( "\n" ); document.write( "Read the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Proving irrationality of some real numbers \r
\n" ); document.write( "\n" ); document.write( "    - What number is greater? Comparing magnitude of irrational numbers \r
\n" ); document.write( "\n" ); document.write( "    - Calculations of expressions containing square roots \r
\n" ); document.write( "\n" ); document.write( "    - Prove that two irrational numbers are equal \r
\n" ); document.write( "\n" ); document.write( "    - Is this number rational or irrational? \r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate expressions involving $\"%28x+%2B+1%2Fx%29\"$ , $\"%28x%5E2%2B1%2Fx%5E2%29\"$ and $\"%28x%5E3%2B1%2Fx%5E3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a square equation\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a cubic and quartic equation\r
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