document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144549>Question 144549</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534386172/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Thank you in advance for help  with this equation. x^2/3+x^1/3-2=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105291 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=105291\">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=x%5E%282%2F3%29%2Bx%5E%281%2F3%29-2=0 ALIGN=MIDDLE  ALT=\"x%5E%282%2F3%29%2Bx%5E%281%2F3%29-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"u=x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2%2Bu-2=0 ALIGN=MIDDLE  ALT=\"u%5E2%2Bu-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"u=x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B2%29%28u-1%29=0 ALIGN=MIDDLE  ALT=\"%28u%2B2%29%28u-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2B2=0 ALIGN=MIDDLE  ALT=\"u%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u-1=0 ALIGN=MIDDLE  ALT=\"u-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-2 ALIGN=MIDDLE  ALT=\"u=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=1 ALIGN=MIDDLE  ALT=\"u=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Now solve for u in each case\r<BR>\n" );
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document.write( "Remember, we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"u=x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29=-2 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29=1 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace \"u\" with  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube both sides in each case\r<BR>\n" );
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document.write( "Notice that when you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > you don't get the correct answer. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an extraneous solution. \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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