document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158710>Question 1158710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference between the squares of two numbers is 21.  Three times the square of the first number increased by the square of the second number is 79.  Find the numbers.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781696 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let the numbers be x and y.  Then the given information is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2+=+21 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2By%5E2+=+79 ALIGN=MIDDLE  ALT=\"3x%5E2%2By%5E2+=+79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It should be obvious what method to use to solve the pair of equations; adding the two equations eliminates y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+=+100 ALIGN=MIDDLE  ALT=\"4x%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-y%5E2+=+21 ALIGN=MIDDLE  ALT=\"25-y%5E2+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+4 ALIGN=MIDDLE  ALT=\"y%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know the square of one of the numbers is 25; but there is no information that lets us determine whether the number is 5 or -5.<br><BR>\n" );
document.write( "Likewise, we know the square of the other number is 4; but we can't tell if that number is 2 or -2.<br><BR>\n" );
document.write( "So we can only say that the two numbers are 5 or -5, and 2 or -2.<br><BR>\n" );
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