document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254489>Question 254489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of Three consecutive even integers is 196. Find the largest of these integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186847 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=186847\">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 <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the largest of 3 consecutive even integers.  The next lower consecutive even integer is then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\,-\,2\">, and the next lower one is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\,-\,4\">.  Add 'em up to get 196:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ (x\ -\ 2)\ +\ (x\ -\ 4)\ =\ 196\">\r<BR>\n" );
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document.write( "Just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">\r<BR>\n" );
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document.write( "The problem is that the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> that satisfies the equation is not an integer, much less an even integer.  Therefore, there is no set of three consecutive even integers such that their sum is 196.\r<BR>\n" );
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document.write( "As further proof, consider:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 62\ +\ 64\ +\ 66\ =\ 192\">\r<BR>\n" );
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document.write( "Note that the sum is smaller than 196, and then next larger sum of three consecutive even integers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 64\ +\ 66\ +\ 68\ =\ 198\">\r<BR>\n" );
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document.write( "has a sum larger than 196.\r<BR>\n" );
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document.write( "Hence the statement: \"The sum of three consecutive even integers is 196.\" is false and the largest of three non-existent integers is also non-existent.\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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