document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197955>Question 197955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers. What are the five integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148430 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <b><i>x</i></b> represent the first integer.  Then the next four consecutive integers are:\r<BR>\n" );
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document.write( "The sum of the squares of the first 3 is equal to the sum of the squares of the next two:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ (x + 1)^2\ +\ (x + 2)^2\ =\ (x + 3)^2\ +\ (x + 4)^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x^2 + 2x + 1\ +\ x^2 + 4x + 4\ =\ x^2 + 6x + 9\ +\ x^2 + 8x + 16\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x^2 + 6x + 5\ =\ 2x^2 + 14x + 25\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 8x - 20\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic (it factors) to determine the first integer.  Exclude the negative root because the problem asks for positive integers.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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