document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199216>Question 1199216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x.\r<BR>\n" );
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document.write( "x^(3/2) - 3x^(1/2) = 0\r<BR>\n" );
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document.write( "sqrt{x^2} - sqrt{3x} = 0\r<BR>\n" );
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document.write( "After squaring both sides, I got x^3 = 3x.\r<BR>\n" );
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document.write( "x^3 - 3x = 0\r<BR>\n" );
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document.write( "x(x^2 - 3) = 0\r<BR>\n" );
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document.write( "x = 0 and x^2 - 3 = 0\r<BR>\n" );
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document.write( "Solving x^2 - 3 = 0 for x, I got sqrt|3}, -sqrt{3}.\r<BR>\n" );
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document.write( "After checking my answers for x, I concludes that the only two solutions<BR>\n" );
document.write( "for x are 0 and sqrt{3}.\r<BR>\n" );
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document.write( "The textbook answers for x are 0 and 3.\r<BR>\n" );
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document.write( "Why am I wrong?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832981 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "On your second line you have replaced <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"3x%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%283x%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Those two expressions are not the same.<br><BR>\n" );
document.write( "Note if you solve by squaring both sides of the equation, you will need to check for extraneous solutions.  Solve by factoring instead.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F2%29-3x%5E%281%2F2%29=0 ALIGN=MIDDLE  ALT=\"x%5E%283%2F2%29-3x%5E%281%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F2%29%29x-3%28%28x%5E%281%2F2%29%29%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%29x-3%28%28x%5E%281%2F2%29%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F2%29%29%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%29%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29=0 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ANSWERS: 0 and 3<br><BR>\n" );
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document.write( "added in response to reader's question....<br><BR>\n" );
document.write( "Extraneous solutions are solutions to an equation you end up with in your work that don't satisfy the original equation.<br><BR>\n" );
document.write( "The most common place where this can happen is if, in the process of solving the original equation, you square both sides at some point.  The extraneous solutions are the result of the fact that the square of a negative number is positive.<br><BR>\n" );
document.write( "For a very simple example, consider the equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29=-3 ALIGN=MIDDLE  ALT=\"sqrt%28x%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know immediately that there is no solution, because a square root is never negative.  But when we square both sides...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But x=9 does not satisfy the original equation.  It is an extraneous root, introduced when we squared both sides of the original equation.<br><BR>\n" );
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