document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175737>Question 175737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the real number solutions of the equation.\r<BR>\n" );
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document.write( "y^4-14y^2+45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130828 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your first problem is that you don't actually have an equation.  There is not an equal sign to be seen anywhere in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-14y%5E2%2B45 ALIGN=MIDDLE  ALT=\"y%5E4-14y%5E2%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So all I can do is assume that you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4+-+14y%5E2+%2B+45+=+0 ALIGN=MIDDLE  ALT=\"y%5E4+-+14y%5E2+%2B+45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Presuming this is the case, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+y%5E2 ALIGN=MIDDLE  ALT=\"t+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then you can write:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+14t+%2B+45+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-+14t+%2B+45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a quadratic that can be solved by ordinary means; this one factors because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-5%29+%2A+%28-9%29+=+45 ALIGN=MIDDLE  ALT=\"+%28-5%29+%2A+%28-9%29+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29+%2B+%28-9%29+=+-14 ALIGN=MIDDLE  ALT=\"%28-5%29+%2B+%28-9%29+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+14t+%2B+45+=+%28t+-+5%29%28t+-+9%29+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-+14t+%2B+45+=+%28t+-+5%29%28t+-+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+5+=+0 ALIGN=MIDDLE  ALT=\"t+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+9+=+0 ALIGN=MIDDLE  ALT=\"t+-+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5 ALIGN=MIDDLE  ALT=\"t+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9 ALIGN=MIDDLE  ALT=\"t+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+y%5E2 ALIGN=MIDDLE  ALT=\"t+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can now say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+5 ALIGN=MIDDLE  ALT=\"y%5E2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%285%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+9 ALIGN=MIDDLE  ALT=\"y%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%289%29+=+3 ALIGN=MIDDLE  ALT=\"y+=+sqrt%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%289%29+=+-3 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%289%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And there are your four real number roots.\r<BR>\n" );
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