document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=594474>Question 594474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two integers is 9 and their product is 18. 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 #376758 by </B><A HREF=/tutors/aboutme.mpl?userid=mamiya><B>mamiya(56)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mamiya><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=376758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x and y be those integers. <BR>\n" );
document.write( " by understanding the question, we know that x*y=18  and x+y=9\r<BR>\n" );
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document.write( "There are many ways to do this ( especially because 9 and 18 are small numbers).\r<BR>\n" );
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document.write( "  First, let's  take one of the easiest ways<BR>\n" );
document.write( "  we need to find two numbers whose sum is 9 , we have (1, 8) (2, 7) (3, 6) (4, 5)<BR>\n" );
document.write( "  Now, we look for the pair of numbers whose product is 18.  Among those pairs of numbers, the only one satisfying our need is (3, 6) so 3 and 6 are those integers.<BR>\n" );
document.write( "  so, the answer is 3 and 6\r<BR>\n" );
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document.write( "  Second way:  <BR>\n" );
document.write( " we need to find two numbers whose product is 18, we have (1, 18) (2, 9) (3, 6)<BR>\n" );
document.write( "Now, we look for the pair of numbers whose sum is 9. Among those pairs , the only one satisfying our need is (3, 6). <BR>\n" );
document.write( " so, the answer is 3 and 6\r<BR>\n" );
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document.write( " Another way :  <BR>\n" );
document.write( "  x* y = 18, x+y = 9 <BR>\n" );
document.write( " consider x+y=9  and write one letter in term of the other one<BR>\n" );
document.write( " x+y=9 -->  x = 9 - y<BR>\n" );
document.write( "now we plug that in the other equation <BR>\n" );
document.write( " x*y = 18 -->  (9-y)y = 18<BR>\n" );
document.write( "          -->  9y - y^2 = 18<BR>\n" );
document.write( "          --> y^2 -9y + 18 = 0<BR>\n" );
document.write( "  y = ( 9 - sqrt(9^2 -4(18)))/2       <BR>\n" );
document.write( "    = ( 9 -sqrt(81 -72))/2             <BR>\n" );
document.write( "    = ( 9 -sqrt9)/2                    <BR>\n" );
document.write( "    = (9-3)/2                         <BR>\n" );
document.write( "    = 3                               <BR>\n" );
document.write( "y = ( 9 + sqrt(9^2 -4(18)))/2  <BR>\n" );
document.write( "  = ( 9 + sqrt(81 -72))/2<BR>\n" );
document.write( "  = ( 9+ sqrt9)/2<BR>\n" );
document.write( "  = (9+3)/2<BR>\n" );
document.write( "  = 6<BR>\n" );
document.write( " With this approach the answer are still 3 and 6 </SPAN>\n" );
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