document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242460>Question 242460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two positive integers differ by 6 and their squares differ by 72. By how much do<BR>\n" );
document.write( "their cubes differ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177479 by </B><A HREF=/tutors/aboutme.mpl?userid=JimboP1977><B>JimboP1977(311)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JimboP1977><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=JimboP1977><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b+=+6 ALIGN=MIDDLE  ALT=\"a-b+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2+=+72 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-b%5E3+=+x ALIGN=MIDDLE  ALT=\"a%5E3-b%5E3+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Well the way I did it which may not be the best, but here goes:\r<BR>\n" );
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document.write( "a^2-a^b can also be written as (a+b)(a-b). We know that a-b = 6\r<BR>\n" );
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document.write( "So (a+b)*6 = 72 so a+b = 72/6 = 12 , 2a-2b = 12.\r<BR>\n" );
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document.write( "So a+b = 2a-2b, so 3b=a. From this we can gather that we are looking for two postive integers with a difference of 6, with one of them 3 times greater than the other.\r<BR>\n" );
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document.write( "The first two numbers that came to mind were 9 and 3. And these are indeed correct.\r<BR>\n" );
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document.write( "So 9^3 - 3^3 = 702  </SPAN>\n" );
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