document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=484238>Question 484238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus 8 is the sum of their squares.\r<BR>\n" );
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document.write( "Thank you very much for the answer ! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331480 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus 8 is the sum of their squares.\r<BR>\n" );
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document.write( "Thank you very much for the answer ! :)\r<BR>\n" );
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document.write( "Let the smaller # be S<BR>\n" );
document.write( "Then the larger # is S + 1\r<BR>\n" );
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document.write( "The sum of the #s is S + S + 1, or 2S + 1<BR>\n" );
document.write( "The difference of the #s is (S + 1) – S or 1 (this is true as they are consecutive #s)\r<BR>\n" );
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document.write( "Product of the sum and difference of the #s = (2S + 1)1, or 2S + 1\r<BR>\n" );
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document.write( "We can now say that: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S+%2B+1+%2B+8+=+S%5E2+%2B+%28S+%2B+1%29%5E2 ALIGN=MIDDLE  ALT=\"2S+%2B+1+%2B+8+=+S%5E2+%2B+%28S+%2B+1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S+%2B+9+=+S%5E2+%2B+S%5E2+%2B+2S+%2B+1 ALIGN=MIDDLE  ALT=\"2S+%2B+9+=+S%5E2+%2B+S%5E2+%2B+2S+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2S%5E2+%2B+2S+-+2S+%2B+1+-+9 ALIGN=MIDDLE  ALT=\"0+=+2S%5E2+%2B+2S+-+2S+%2B+1+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%5E2+-+8+=+0 ALIGN=MIDDLE  ALT=\"2S%5E2+-+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28S%5E2+-+4%29+=+2%280%29 ALIGN=MIDDLE  ALT=\"2%28S%5E2+-+4%29+=+2%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2+-+4+=+0 ALIGN=MIDDLE  ALT=\"S%5E2+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(S + 2)(S – 2) = 0\r<BR>\n" );
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document.write( "S = - 2 (ignore as answer has to be a positive number) or S = 2 \r<BR>\n" );
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document.write( "Since S, or smaller number is 2, then the numbers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282_and_+3%29 ALIGN=MIDDLE  ALT=\"highlight_green%282_and_+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "---------<BR>\n" );
document.write( "Check<BR>\n" );
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document.write( "Sum of 2 and 3: 5 (2 + 3)\r<BR>\n" );
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document.write( "Difference of 2 and 3: 1 (3 - 2)\r<BR>\n" );
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document.write( "Product of sum and difference: 5 (5 * 1)\r<BR>\n" );
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document.write( "Product of the sum and difference of the numbers plus 8 is the sum of their squares is as follows:\r<BR>\n" );
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document.write( "5 + 8 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2+%2B+3%5E2 ALIGN=MIDDLE  ALT=\"2%5E2+%2B+3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "13 = 4 + 9\r<BR>\n" );
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document.write( "13 = 13 (TRUE)\r<BR>\n" );
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