document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825271>Question 825271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497174 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is somewhat ambiguous, but here is a try.\r<BR>\n" );
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document.write( "x and y are the natural numbers to find.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=4 ALIGN=MIDDLE  ALT=\"x%2By=4\"   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%2By%5E2-9%28x%2By%29=8 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-9%28x%2By%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The sum of just the two numbers can be substituted to give <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-9%2A4=8 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-9%2A4=8\"   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%2By%5E2-36-8=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-36-8=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%5E2%2By%5E2=44 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going back to x+y=4, y=4-x, so substitute into the circle equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%284-x%29%5E2=44 ALIGN=MIDDLE  ALT=\"x%5E2%2B%284-x%29%5E2=44\"   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%2B16-8x%2Bx%5E2=44 ALIGN=MIDDLE  ALT=\"x%5E2%2B16-8x%2Bx%5E2=44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B16-44=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B16-44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x-28=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8x-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E2-4x-14=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E2-4x-14=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "'<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2B-+sqrt%2872%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%284%2B-+sqrt%2872%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  unless I made a mistake, this value will not be a Natural Number.  Neither will be y Natural. </SPAN>\n" );
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