document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289894>Question 289894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty figuring this problem out.  Could you please help me?  :)\r<BR>\n" );
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document.write( "16x^4-41x^2+25=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209879 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sure I can help. What have you tried? Where is your work?<BR>\n" );
document.write( "There are four real answers two are negatives of the other two<BR>\n" );
document.write( "You might guess that 16 (4^2) and 25 (5^2) has something to do with 2 of the roots.\r<BR>\n" );
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document.write( "Notice that 41=25+16<BR>\n" );
document.write( "There might be some difference of squares involved since one answer is a negative of the other.<BR>\n" );
document.write( "remember (a-b)*(a+b)=a^2-b^2<BR>\n" );
document.write( "(4x-5)(4x+5)=16x^2-25<BR>\n" );
document.write( "divide that into 16x^4-41x+25 gets<BR>\n" );
document.write( "(x^2-1)<BR>\n" );
document.write( "but that equals (x-1)*(x+1)<BR>\n" );
document.write( "so we have (4x-5)*(4x+5)*(x-1)*(x+1)\r<BR>\n" );
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document.write( "We were very lucky<BR>\n" );
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