document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320442>Question 320442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two positive integers have a sum of 21 and a product of 108. what are the integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229516 by </B><A HREF=/tutors/aboutme.mpl?userid=Sunny+Day><B>Sunny Day(15)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Sunny+Day><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let one integer be x<BR>\n" );
document.write( "Then the second integer = 21 - x.\r<BR>\n" );
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document.write( "Their product = 108<BR>\n" );
document.write( "ie. x(21-x) = 108<BR>\n" );
document.write( "21x - x^2 = 108<BR>\n" );
document.write( "21x - x^2 - 108 = 0<BR>\n" );
document.write( "-x^2 + 21x - 108 = 0<BR>\n" );
document.write( "Multiplying the whole with -1, (in order to make the co-efficient of x^2 +ve)\r<BR>\n" );
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document.write( "x^2 - 21x + 108 = 0 -------- (1)\r<BR>\n" );
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document.write( "[Now we have to find two numbers such that their product is 108 and sum is -21. and these two numbers will eb factors of 108. They are -9 and -12]\r<BR>\n" );
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document.write( "So (1) can be written as<BR>\n" );
document.write( "x^2 - 9x - 12x + 108 = 0<BR>\n" );
document.write( "x(x-9) - 12(x-9) = 0<BR>\n" );
document.write( "(x-9) (x-12) = 0<BR>\n" );
document.write( "So either x-9 = 0   or x-12 = 0<BR>\n" );
document.write( "           x = 9    or  x = 12<BR>\n" );
document.write( "These are the required integers </SPAN>\n" );
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