document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194290>Question 1194290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers differ by 8 and their name product is 209. Find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826452 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Notice that, in the formal algebraic solution from @boreal, you have to factor a quadratic expression by finding two numbers whose difference is 8 and whose product is 209.<br><BR>\n" );
document.write( "But that is exactly what the original problem asks you to do -- so that formal algebraic method doesn't help you get any closer to the answer.<br><BR>\n" );
document.write( "If you need a formal algebraic solution, use the nice \"trick\" shown by tutor @ikleyn.  As she says in her response, it is a very useful method applicable to many problems.<br><BR>\n" );
document.write( "But if formal algebra is not required, clearly the fastest way to the answer is to find how the product 209 factors.<br><BR>\n" );
document.write( "209 = 11*19<br><BR>\n" );
document.write( "So the two numbers are 11 and 19.<br><BR>\n" );
document.write( "Then, since the problem allows negative answers, another solution is -11 and -19.<br><BR>\n" );
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