document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3585>Question 3585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help<BR>\n" );
document.write( "(x^2+2x)^2-5(x^2+2x)+6=0\r<BR>\n" );
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document.write( "           and\r<BR>\n" );
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document.write( "x^1/2-11x^1/4+30\r<BR>\n" );
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document.write( "          and\r<BR>\n" );
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document.write( "6x^3/5-24=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1597 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=1597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  (I) (x^2+2x)^2-5(x^2+2x)+6=0<BR>\n" );
document.write( "   Let y = x^2+2x, then the given equation is converted to<BR>\n" );
document.write( "    y^2 - 5y + 6 =0,<BR>\n" );
document.write( "   Factor: (y-2)(y-3) = 0<BR>\n" );
document.write( "    so, y= 2 or 3.<BR>\n" );
document.write( "   That is, x^2+2x = 2 or x^2+2x = 3,<BR>\n" );
document.write( "   Hence x^2+2x - 2 = 0, <BR>\n" );
document.write( "   By quadratic formula, x= -1 + sqrt(3) or  -1 - sqrt(3)<BR>\n" );
document.write( "   Or x^2+2x - 3 = 0, <BR>\n" );
document.write( "   Factor: (x-1)(x+3) =0, so x = 1 or -3 [Four solutions of x]\r<BR>\n" );
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document.write( " (II) x^1/2-11x^1/4+30<BR>\n" );
document.write( "  Let u = x^1/4, then we have<BR>\n" );
document.write( "   u^2 - 11 u + 30 = 0,<BR>\n" );
document.write( "  Factor: (u-6)(u-5) =0, so u = 6 or 5.<BR>\n" );
document.write( "  When  u=6 , x^1/4 = 6, x = 6^4 = 36^2 = 1296<BR>\n" );
document.write( "  When  u=5 , x^1/4 = 5, x = 5^4 = 25^2 = 625.\r<BR>\n" );
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document.write( " (III) 6x^3/5-24=0<BR>\n" );
document.write( "  Cancel 6:  x^3/5-4=0, <BR>\n" );
document.write( "  Or x^3/5 = 4<BR>\n" );
document.write( "  So, x = 4^(5/3) = 4 * 4^(2/3) = 4 * (2^4)^(1/3)<BR>\n" );
document.write( "      = 4*2 * 2^(1/3) = 8* 2^(1/3)<BR>\n" );
document.write( " <BR>\n" );
document.write( " Try to check the above answers yourself.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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