document.write( "Question 1208097: If x + 1/x = √3
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Algebra.Com's Answer #846253 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If x + 1/x = $\"sqrt%283%29\"$ , find the value of x^18 + x^12 + 1.
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document.write( "If  x + 1/x = , then\r\n" );
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document.write( "     + 1 = \r\n" );
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document.write( "     -  + 1 = 0.\r\n" );
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document.write( "It is the general form of a quadratic equation  ax^2 + bx + c = 0\r\n" );
document.write( "with a= 1, b= , c= 1.\r\n" );
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document.write( "Apply the quadratic formula to find the roots\r\n" );
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document.write( "     =  =  =  =  = .\r\n" );
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document.write( "So,   =  = ;\r\n" );
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document.write( "      =  = .\r\n" );
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document.write( "Thus    is a complex number with the modulus of 1 and the argument of  .\r\n" );
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document.write( "        is a complex number with the modulus of 1 and the argument of  .\r\n" );
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document.write( "For  x =  = ,  we have  \r\n" );
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document.write( "      +  + 1 =  +  + 1 =  +  + 1 = -1 + 1 + 1 = 1.\r\n" );
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document.write( "For  x =  = ,  we have  \r\n" );
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document.write( "      +  + 1 =  +  + 1 =  +  + 1 = -1 + 1 + 1 = 1.\r\n" );
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document.write( "So, for both values of roots, we have   +  + 1 = 1.\r\n" );
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document.write( "At this point, the solution is complete.\r\n" );
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document.write( "ANSWER.  If  x + 1/x = ,  then   +  + 1 = 1.\r\n" );
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