document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120936>Question 1120936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a^3+12ab^2=679 and 9a^2b+12b^3=978, find (a-2b)^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736895 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I looked at this problem several times before I realized how easy it was, with the help of a graphing calculator....<br><BR>\n" );
document.write( "The given equations suggest that a and b are both integers, probably positive.<br><BR>\n" );
document.write( "So solve the first equation for b in terms of a; then use a graphing calculator table to find an integer value of a that gives a perfect square integer value for b^2.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+%28679-a%5E3%29%2F%2812a%29 ALIGN=MIDDLE  ALT=\"b%5E2+=+%28679-a%5E3%29%2F%2812a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "My TI-83 calculator shows b^2=4 when a = 7; the apparent solution is a=7 and b=2.<br><BR>\n" );
document.write( "Plugging those values in the two given equations confirms the answer.<br><BR>\n" );
document.write( "So the answer to the problem is:<BR>\n" );
document.write( "(a-2b)^2 = (7-4)^2 = 9 </SPAN>\n" );
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