document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206122>Question 1206122</A>: <I><SPAN STYLE=\"word-break: break-all;\">   If a+1/3a=2 then find the value of 9a^2+1/a^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843363 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=843363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll assume the given equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+1%2F%283a%29+=+2 ALIGN=MIDDLE  ALT=\"a+%2B+1%2F%283a%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And I'll assume you want to find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%5E2+%2B+1%2F%28a%5E2%29 ALIGN=MIDDLE  ALT=\"9a%5E2+%2B+1%2F%28a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Please let me know if otherwise.\r<BR>\n" );
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document.write( "If my assumptions are correct, then you should be careful to use parenthesis.<BR>\n" );
document.write( "Something like a + 1/3a could be misinterpreted as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B%281%2F3%29a ALIGN=MIDDLE  ALT=\"a%2B%281%2F3%29a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So instead of a + 1/3a, you should type in a + 1/(3a)<BR>\n" );
document.write( "Instead of 9a^2+1/a^2, you should type in 9a^2+1/(a^2)\r<BR>\n" );
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document.write( "The original equation just involves 'a' without any exponent.<BR>\n" );
document.write( "The thing we want to find has 'a' being squared.<BR>\n" );
document.write( "A naive approach could be to simply square both sides to see what happens.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+1%2F%283a%29+=+2 ALIGN=MIDDLE  ALT=\"a+%2B+1%2F%283a%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B+1%2F%283a%29%29%5E2+=+2%5E2 ALIGN=MIDDLE  ALT=\"%28a+%2B+1%2F%283a%29%29%5E2+=+2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+2%2Aa%2A%281%2F%283a%29%29+%2B+%281%2F%283a%29%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+2%2Aa%2A%281%2F%283a%29%29+%2B+%281%2F%283a%29%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use formula (p+q)^2 = p^2+2pq+q^2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+2%2F3+%2B+1%2F%289a%5E2%29+=+4 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+2%2F3+%2B+1%2F%289a%5E2%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > The 'a's cancel out in the middle portion.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1%2F%289a%5E2%29+=+4+-+2%2F3 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1%2F%289a%5E2%29+=+4+-+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1%2F%289a%5E2%29+=+10%2F3 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1%2F%289a%5E2%29+=+10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "We want to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%5E2+%2B+1%2F%28a%5E2%29 ALIGN=MIDDLE  ALT=\"9a%5E2+%2B+1%2F%28a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1%2F%289a%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1%2F%289a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left hand side.<BR>\n" );
document.write( "The coefficients for the a^2 terms (1 and 9) have been swapped. <BR>\n" );
document.write( "A quick easy fix is to multiply both sides by 9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1%2F%289a%5E2%29+=+10%2F3 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1%2F%289a%5E2%29+=+10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A%28a%5E2+%2B+1%2F%289a%5E2%29%29+=+9%2A10%2F3 ALIGN=MIDDLE  ALT=\"9%2A%28a%5E2+%2B+1%2F%289a%5E2%29%29+=+9%2A10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%5E2+%2B+9%2A%281%2F%289a%5E2%29%29+=+90%2F3 ALIGN=MIDDLE  ALT=\"9a%5E2+%2B+9%2A%281%2F%289a%5E2%29%29+=+90%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%5E2+%2B+1%2F%28a%5E2%29+=+30 ALIGN=MIDDLE  ALT=\"9a%5E2+%2B+1%2F%28a%5E2%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer: <font color=red size=4>30</font><BR>\n" );
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