document.write( "Question 1036823: if (x+1/x)^2 = 3 then find the value of x^206 + x^200 + x^90 + x^84 + x^18 + x^12 + x^6 + 1 \n" ); document.write( "

Algebra.Com's Answer #651542 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "if (x+1/x)^2 = 3 then find the value of x^206 + x^200 + x^90 + x^84 + x^18 + x^12 + x^6 + 1
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\n" ); document.write( "\n" ); document.write( "Answer. If $\"%28x%2B1%2Fx%29%5E2\"$ = $\"3\"$ then the value of $\"x%5E206+%2B+x%5E200+%2B+x%5E90+%2B+x%5E84+%2B+x%5E18+%2B+x%5E12+%2B+x%5E6+%2B+1\"$ is zero.\r
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document.write( "If   =   then\r\n" );
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document.write( " +  +  = ,\r\n" );
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document.write( " +  = ,\r\n" );
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document.write( " = ,   ( <--- Introduce new variable u =  )  ---> \r\n" );
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document.write( " = ,   ( <---multiply both sides by u)  ---> \r\n" );
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document.write( " = ,    ( <--- solve by using the quadratic formula )  ---> \r\n" );
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document.write( " =  = ,   --->\r\n" );
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document.write( " = .   ( since x =  )\r\n" );
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document.write( "In other words, if   =   then x is the primitive root of the degree 12 of 1.\r\n" );
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document.write( "Then\r\n" );
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document.write( " = ,  so   = ;\r\n" );
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document.write( " = ,  so   = ;\r\n" );
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document.write( " = ,  so   = ,  and also\r\n" );
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document.write( " = ,  so   = .\r\n" );
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document.write( "Hence,  the value of  is zero.\r\n" );
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Solved.\r
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