document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837473>Question 837473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference of two integers is 9. The sum of their square is 261. find the two integers\r<BR>\n" );
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document.write( "n-m=9<BR>\n" );
document.write( "n^2 + m^2 = 261<BR>\n" );
document.write( "n^2 + 2mn + m^2 = 261<BR>\n" );
document.write( " that is all I got<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504612 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You were correct in setting up the two equations:  n-m=9 and n^2 + m^2 = 261.  Now, you will need to solve the second equation (n^2 + m^2 = 261) by rewriting the first equation (n - m = 9).  You can either solve for n or m.  For this, we will solve for n, which gives us n = 9 + m.  We will now substitute 9 + m for n in equation 2, giving us the following:\r<BR>\n" );
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document.write( "(9 + m)^2 + m^2 = 261\r<BR>\n" );
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document.write( "We can expand (9 + m)^2.  This will give us:  81 + 18m + m^2.  We now have:\r<BR>\n" );
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document.write( "81 + 18m + m^2 + m^2 = 261.  Combining like terms will give us:\r<BR>\n" );
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document.write( "81 + 18m + 2m^2 = 261\r<BR>\n" );
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document.write( "Next, we will subtract 261 from both sides of the equal sign, which will give us:\r<BR>\n" );
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document.write( "-261 + 81 + 18m + 2m^2 = 0\r<BR>\n" );
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document.write( "Once again, we will combine like terms, giving us:\r<BR>\n" );
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document.write( "-180 + 18m + 2m^2 = 0\r<BR>\n" );
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document.write( "I want to simplify this equation to make it easier to solve, so, since -180, 18, and 2 are all divisible by 2, I will divide all of these by 2, giving us:\r<BR>\n" );
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document.write( "-90 + 9m + m^2 = 0\r<BR>\n" );
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document.write( "Let's rearrange to put this in standard form:  m^2 + 9m - 90 = 0\r<BR>\n" );
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document.write( "We can factor this equation, since the factors of -90 that multiply to give us -90 and add together to give us 9 are 15 and -6.  This gives us:\r<BR>\n" );
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document.write( "(m + 15)(m - 6) = 0\r<BR>\n" );
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document.write( "This gives us:  m = -15 and 6.  Remember, we are looking for integers, and -15 is not an integer.  Therefore, 6 is one of our integers.  To find our other integer, simply replace m in our rewritten equation 1 (n = 9 + m), with 6:\r<BR>\n" );
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document.write( "n = 9 + 6, which gives us n = 15.\r<BR>\n" );
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document.write( "Therefore our two integers are 6 and 15 </SPAN>\n" );
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