document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=45041>Question 45041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the squares of two consecutive even integers 1252. find the inetegers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29866 by </B><A HREF=/tutors/aboutme.mpl?userid=abhijitvakil><B>abhijitvakil(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=abhijitvakil><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=29866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the lesser integer be x. Then the other number being consecutive even integer to x, becomes (x + 2). Now the relation given in the problem can be stated as :\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + (x + 2)^2 = 1252\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + (x^2 + 2*x*2 + 2^) = 1252  ( we use the formula (a + b)^2 = a^2 + 2ab + b^2) \r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + x^2 + 4x + 4 = 1252\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "2x^2 + 4x + 4 - 1252 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 2x - 624 = 0 ..... (1)    ( we divide the entire equation by 2)\r<BR>\n" );
document.write( "\n" );
document.write( "The above is a typical quadratic equation of the type ax^2 + bx + c = 0. Thus we have\r<BR>\n" );
document.write( "\n" );
document.write( "a = 1, b = 2 & c = 624\r<BR>\n" );
document.write( "\n" );
document.write( "The solution to this equation is given by the following :\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substituting the values of a,b, & c into the above, we get two \"roots\" or solutions to x ( i am skipping the numerical calculations, which the student can do himself ):\r<BR>\n" );
document.write( "\n" );
document.write( "x = (24, -26)\r<BR>\n" );
document.write( "\n" );
document.write( "Thus if x = 24, then the other integer will be x+2 i.e. 26, and if x = -26, then the other integer will be -26+2 i.e. -24. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );