document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389639>Question 389639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers whose sum is 17 and whose squares total 145 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276152 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=276152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The easiest way is probably to guess and check, since it is likely that both numbers will be integers. Guessing and checking, the numbers are 9 and 8.\r<BR>\n" );
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document.write( "Or, we can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%2B+q+=+17 ALIGN=MIDDLE  ALT=\"p+%2B+q+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+%2B+q%5E2 ALIGN=MIDDLE  ALT=\"p%5E2+%2B+q%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 145. Squaring the first equation,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p+%2B+q%29%5E2+=+p%5E2+%2B+2pq+%2B+q%5E2+=+289 ALIGN=MIDDLE  ALT=\"%28p+%2B+q%29%5E2+=+p%5E2+%2B+2pq+%2B+q%5E2+=+289\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pq+=+144 ALIGN=MIDDLE  ALT=\"2pq+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pq+=+72 ALIGN=MIDDLE  ALT=\"pq+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If we assume that p and q are roots of a polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"x%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, use Vieta's formula:\r<BR>\n" );
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document.write( "The sum of the roots is -b --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%2B+q+=+17+=+-b ALIGN=MIDDLE  ALT=\"p+%2B+q+=+17+=+-b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The product of the roots is c --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pq+=+72+=+c ALIGN=MIDDLE  ALT=\"pq+=+72+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This implies b = -17 and c = 72, so p and q are roots of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+17x+%2B+72 ALIGN=MIDDLE  ALT=\"x%5E2+-+17x+%2B+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The polynomial can be factored as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+8%29%28x+-+9%29 ALIGN=MIDDLE  ALT=\"%28x+-+8%29%28x+-+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so p,q = (8,9). </SPAN>\n" );
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