document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151226>Question 1151226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose x + (1 / x) = 1<BR>\n" );
document.write( "Compute the value of (x^1613) + (x^-1613)\r<BR>\n" );
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document.write( "A) 1 / x<BR>\n" );
document.write( "B) -1 / 1613<BR>\n" );
document.write( "C) x<BR>\n" );
document.write( "D) 1 / 1613<BR>\n" );
document.write( "E) 3<BR>\n" );
document.write( "F) 1 / (x^-1613)<BR>\n" );
document.write( "G) 2<BR>\n" );
document.write( "H) 1 / (x^1613)<BR>\n" );
document.write( "I) none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772910 by </B><A HREF=/tutors/aboutme.mpl?userid=pavan+sai+reddy><B>pavan sai reddy(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pavan+sai+reddy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the answer needs to be 1. I think this is from \"complex numbers\" question if the quadratic is in the form x^2-x+1=0 the roots are -omega ,-omega^2. I think with this stuff the problem can be cracked                                     \r<BR>\n" );
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document.write( "               x+1/x=1<BR>\n" );
document.write( "         =>x^2-x+1=0<BR>\n" );
document.write( "         => x=-omega,-omega^2 (roots of the equation)<BR>\n" );
document.write( "         Given that,<BR>\n" );
document.write( "            x^1613+1/x^1613<BR>\n" );
document.write( "                <BR>\n" );
document.write( "               [splitting the x^1613 into (x^1611)(x^2)]\r<BR>\n" );
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document.write( "                [now replace x with -omega ]    <BR>\n" );
document.write( "                   <BR>\n" );
document.write( "       [ properties:- <BR>\n" );
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document.write( "                1)omega^2+omega+1=0<BR>\n" );
document.write( "                 <BR>\n" );
document.write( "                2) omega^3n=1         ]      \r<BR>\n" );
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document.write( "         =>  (-omega)^1611(-omega)^2 + 1/(-omega)^1611(-omega)^2\r<BR>\n" );
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document.write( "         => -omega^2-1/omega^2<BR>\n" );
document.write( "     <BR>\n" );
document.write( "         =>  -(omega^4+1)/omega^2\r<BR>\n" );
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document.write( "                                   (property 2 )     <BR>\n" );
document.write( "         => -(omega+1)/omega^2<BR>\n" );
document.write( "                                    <BR>\n" );
document.write( "         =>  -(-omega^2)/omega^2    (property 1)\r<BR>\n" );
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document.write( "         => omega^2/omega^2   => 1(ans)\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
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