document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408068>Question 408068</A>: <I><SPAN STYLE=\"word-break: break-all;\">  1)Use the Cauchy - Schwarz inequality to solve x3   &#9472;  25x2  &#9472;   4x + 100 = 0, given that all its roots are rational.				      (5 Marks                  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287525 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't really see how the Cauchy-Schwarz inequality applies to this problem...from what I know, the Cauchy-Schwarz inequality says that for positive numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bi%5D ALIGN=MIDDLE  ALT=\"a%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bi%5D ALIGN=MIDDLE  ALT=\"b%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3C=+i+%3C=+n ALIGN=MIDDLE  ALT=\"1+%3C=+i+%3C=+n\"   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=sum%28a%5Bi%5D%5E2%2C+i+=+1%2C+n%29sum%28b%5Bi%5D%5E2%2C+i+=+1%2C+n%29+%3E=+sum%28a%5Bi%5Db%5Bi%5D%2C+i+=+1%2C+n%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The best way is to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+25 ALIGN=MIDDLE  ALT=\"x+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > out, leaving\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+25%29%28x%5E2+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+25%29%28x%5E2+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From here, it is apparent that x = 25, -2, or 2. </SPAN>\n" );
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