document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31323>Question 31323</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I'm trying to find all real solutions to this equation:\r<BR>\n" );
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document.write( "4x^-4-16x^-2+4=0\r<BR>\n" );
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document.write( "I have:<BR>\n" );
document.write( "4/x^4-16/x^2+4=0<BR>\n" );
document.write( "multiplying by x^4:<BR>\n" );
document.write( "4-16x^2+4=0<BR>\n" );
document.write( "4x^4-16x^2+4=0<BR>\n" );
document.write( "4(x^4-4x^2+1) = 0 (unfactorable?)<BR>\n" );
document.write( "a=1;b=4;c=1\r<BR>\n" );
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document.write( "Using the quadratic equation I get:<BR>\n" );
document.write( "-4+-sq root of 3, but this doesn't seem right.<BR>\n" );
document.write( "Thanks for all your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18046 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you had an error with your signs half way through...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E-4-16x%5E-2%2B4=0+ ALIGN=MIDDLE  ALT=\"+4x%5E-4-16x%5E-2%2B4=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Fx%5E4-16%2Fx%5E2%2B4=0+ ALIGN=MIDDLE  ALT=\"+4%2Fx%5E4-16%2Fx%5E2%2B4=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4-16x%5E2%2B4x%5E4=0+ ALIGN=MIDDLE  ALT=\"+4-16x%5E2%2B4x%5E4=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E4-16x%5E2%2B4=0+ ALIGN=MIDDLE  ALT=\"+4x%5E4-16x%5E2%2B4=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%5E4-4x%5E2%2B1=0+ ALIGN=MIDDLE  ALT=\"+x%5E4-4x%5E2%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this doesn't factorise simply. So lets use the quadratic formula.\r<BR>\n" );
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document.write( "First however, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2-4y%2B1=0+ ALIGN=MIDDLE  ALT=\"+y%5E2-4y%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2+-+4%281%29%281%29%29%29%2F%282%281%29%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2+-+4%281%29%281%29%29%29%2F%282%281%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284+%2B-+sqrt%2816+-+4%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%284+%2B-+sqrt%2816+-+4%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284+%2B-+sqrt%2812%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%284+%2B-+sqrt%2812%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284+%2B-+sqrt%284%2A3%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%284+%2B-+sqrt%284%2A3%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284+%2B-+sqrt%284%29sqrt%283%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%284+%2B-+sqrt%284%29sqrt%283%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284+%2B-+2sqrt%283%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%284+%2B-+2sqrt%283%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%282%282+%2B-+sqrt%283%29%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%282%282+%2B-+sqrt%283%29%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2+%2B-+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+y+=+2+%2B-+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2+%2B+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+y+=+2+%2B+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2+-+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+y+=+2+-+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence, from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+sqrt%282+%2B+sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+sqrt%282+%2B+sqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-sqrt%282+%2B+sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+-sqrt%282+%2B+sqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+sqrt%282+-+sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+sqrt%282+-+sqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-sqrt%282+-+sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+-sqrt%282+-+sqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );