document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828975>Question 828975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i want the value of x in (x+ 1/x)^2=3 and then show by submitting the x value in the equation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499598 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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/cgi-bin/show-face.mpl?user=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+1%2Fx%29%5E2=3 ALIGN=MIDDLE  ALT=\"%28x%2B+1%2Fx%29%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take square root of each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+1%2Fx%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"%28x%2B+1%2Fx%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply each side by x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B+1%29=sqrt%283%29x ALIGN=MIDDLE  ALT=\"%28x%5E2%2B+1%29=sqrt%283%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract sqrt(3)x from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-sqrt%283%29x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2-sqrt%283%29x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solutions are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F2%29%28sqrt%283%29-i%29 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29%28sqrt%283%29-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F2%29%28sqrt%283%29%2Bi%29 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29%28sqrt%283%29%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "See http://www.wolframalpha.com/input/?i=x^2-sqrt%283%29x%2B1%3D0\r<BR>\n" );
document.write( "\n" );
document.write( "below is the solution by the solver<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1.73205080756888x%2B1+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1.73205080756888x%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-1.73205080756888%29%5E2-4%2A1%2A1=-0.99999999999999 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1.73205080756888%29%5E2-4%2A1%2A1=-0.99999999999999\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -0.99999999999999 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -0.99999999999999 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+0.99999999999999%29+=+0.999999999999995 ALIGN=MIDDLE  ALT=\"sqrt%28+0.99999999999999%29+=+0.999999999999995\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--1.73205080756888%2B-+i%2Asqrt%28+-0.99999999999999+%29%29%2F2%5C1+=++%28--1.73205080756888%2B-+i%2A0.999999999999995%29%2F2%5C1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1.73205080756888%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1.73205080756888%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plugging solutions back into the equation will take some careful work. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );