document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095691>Question 1095691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two positive numbers, which have a difference of 3, are squared. The difference in the results is 81. Find the two numbers with working. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710210 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a be the larger number<BR>\n" );
document.write( "let b be the smaller number\r<BR>\n" );
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document.write( "a - b = 3\r<BR>\n" );
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document.write( "a^2 - b^2 = 81\r<BR>\n" );
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document.write( "since a^2 - b^2 is equal to (a - b) * (a + b), then:\r<BR>\n" );
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document.write( "(a - b) * (a + b) = 81\r<BR>\n" );
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document.write( "since a - b = 3, then:\r<BR>\n" );
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document.write( "3 * (a + b) = 81\r<BR>\n" );
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document.write( "since a - b = 3, then a = b + 3 then:\r<BR>\n" );
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document.write( "3 * (a + b) = 81 becomes 3 * (b + 3 + b) = 81\r<BR>\n" );
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document.write( "simplify to get 3 * (2b + 3) = 81\r<BR>\n" );
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document.write( "simplify further to get 6b + 9 = 81\r<BR>\n" );
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document.write( "solve for b to get b = (81 - 9) / 6 = 12\r<BR>\n" );
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document.write( "since a = b + 3, then a = 15\r<BR>\n" );
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document.write( "your larger number is 15 and your smaller number is 12.\r<BR>\n" );
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document.write( "15 - 12 = 3\r<BR>\n" );
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document.write( "15^2 - 12^2 = 225 - 144 = 81\r<BR>\n" );
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document.write( "your solution is that the two number are 15 and 12.\r<BR>\n" );
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