document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087364>Question 1087364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a^2 + 1 = a find the value of a^3.<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 #701628 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=701628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1+=+a ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+1-1+=+a-1 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1-1+=+a-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+a-1 ALIGN=MIDDLE  ALT=\"a%5E2+=+a-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Call this equation (1)\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+=+a ALIGN=MIDDLE  ALT=\"a%5E2+%2B+1+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the original equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%28a%5E2+%2B+1%29+=+a%2Aa ALIGN=MIDDLE  ALT=\"a%2A%28a%5E2+%2B+1%29+=+a%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 'a'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2B+a+=+a%5E2 ALIGN=MIDDLE  ALT=\"a%5E3+%2B+a+=+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2B+a-a+=+a%5E2-a ALIGN=MIDDLE  ALT=\"a%5E3+%2B+a-a+=+a%5E2-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 'a' from both sides to isolate the a^3 term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+a%5E2+-+a ALIGN=MIDDLE  ALT=\"a%5E3+=+a%5E2+-+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplfy\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+a-1+-+a ALIGN=MIDDLE  ALT=\"a%5E3+=+a-1+-+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-1 ALIGN=MIDDLE  ALT=\"a-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. See equation (1) above.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+-1 ALIGN=MIDDLE  ALT=\"a%5E3+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Note how the 'a' terms on the right side cancel out\r<BR>\n" );
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document.write( "An alternative is to solve for 'a' using the quadratic formula (after you get everything to one side and have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-a%2B1+=+0 ALIGN=MIDDLE  ALT=\"a%5E2-a%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >). That leads to two complex solutions in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bbi ALIGN=MIDDLE  ALT=\"a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. After cubing both sides of the two equations you'll lead to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+-1 ALIGN=MIDDLE  ALT=\"a%5E3+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This method is a lot longer than the first method so I find it ideal to follow the first method. \r<BR>\n" );
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document.write( "No matter which method you follow, the <font color=red>final answer is -1</font></font> </SPAN>\n" );
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