document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182485>Question 182485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FIND TWO CONSECUTIVE INTEGERS IF TWO TIMES THE SQUARE OF THE FIRST IS EQUAL TO 23 MORE THAN THE SQUARE OF THE SECOND... thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136964 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=136964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+4\"><BR>\n" );
document.write( "PLEASE DO NOT TYPE YOUR QUESTION IN ALL CAPITALS.  IT IS THE ELECTRONIC EQUIVALENT OF SHOUTING, THEREFORE BOTH RUDE AND ANNOYING.\r<BR>\n" );
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document.write( "If the first integer is <i>x</i>, then the next consecutive integer is <i>x</i> + 1.\r<BR>\n" );
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document.write( "Two times the square of the first integer: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x^2\">\r<BR>\n" );
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document.write( "23 more than the square of the second integer: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x + 1)^2 + 23\">\r<BR>\n" );
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document.write( "These two expressions are equal so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2x^2 = (x + 1)^2 + 23\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2x^2 = x^2 + 2x + 1 + 23\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x^2 - 2x - 24 = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math -6 \times 4 = -24\"> and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math -6 + 4 = -2\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math (x - 6)(x + 4) = 0\">\r<BR>\n" );
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document.write( "Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x - 6 = 0 \ \ \Rightarrow\ \ x = 6\"> or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x + 4 = 0 \ \ \Rightarrow\ \ x = -4\">\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2(-4)^2 = 32\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math (-4 + 1)^2 + 23 = 9 + 23 = 32\"> Checks.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2(6)^2 = 72\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math (6 + 1)^2 + 23 = 49 + 23 = 72\"> Checks.\r<BR>\n" );
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document.write( "So the required integers are either -4 and -3 or 6 and 7.\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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