document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235999>Question 235999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two consecutive positive odd integers is one less than three times their sum. Find the integers.\r<BR>\n" );
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document.write( "A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 feet. Find the length of the ladder if the length is 8 feet more than its distance from the wall.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173760 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=173760\">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 a positive odd integer.  Then the next consecutive positive odd integer must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\">.\r<BR>\n" );
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document.write( "The product:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x(x\ +\ 2)\ =\ x^2\ +\ 2x\">\r<BR>\n" );
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document.write( "The sum:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ x\ +\ 2\ =\ 2x\ + 2\">\r<BR>\n" );
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document.write( "One less than that:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\ + 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ =\ 2x\ +\ 1\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic (it factors).  Exclude the negative root because the problem asked for positive odd integers.  The positive root is one of the integers.  Add 2 to get the other one.\r<BR>\n" );
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document.write( "The ladder, the ground, and the wall, presuming that the wall and the ground form a right angle, form a right triangle with sides 12, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 8\">, and hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">\r<BR>\n" );
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document.write( "Mr. Pythagoras says:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ (x\ -\ 8)^2\ + 144\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">\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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