document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209770>Question 1209770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all (real or nonreal) x satisfying<BR>\n" );
document.write( "(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850274 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Find all (real or nonreal) x satisfying<BR>\n" );
document.write( "(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution in the post by @CPhill is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28INCORRECT%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28INCORRECT%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "@CPhill deduced this equation to \r<BR>\n" );
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document.write( "    7a^4 + 34a^3 + 12a^2 - 34a + 5 = 0\r\n" );
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document.write( "    **2. Factor the Equation:**\r\n" );
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document.write( "    Notice that the coefficients are symmetric.    <<<---=== This is WRONG: coefficients are not symmetric,\r\n" );
document.write( "    This suggests that we can factor by grouping.  <<<---===  Therefore, this method of reducing to quadratic equation \r\n" );
document.write( "                                                              DOES NOT work and, therefore, is INCORRECT.\r\n" );
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document.write( "    Let's divide by a^2:\r\n" );
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document.write( "    7a^2 + 34a + 12 - 34/a + 5/a^2 = 0\r\n" );
document.write( "    7(a^2 + 5/7a^2) + 34(a - 1/a) + 12 = 0\r\n" );
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document.write( "    Let b = a - 1/a. Then b^2 = a^2 - 2 + 1/a^2, so a^2 + 1/a^2 = b^2 + 2\r\n" );
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document.write( "    7(b^2 + 2) + 34b + 12 = 0\r\n" );
document.write( "    7b^2 + 14 + 34b + 12 = 0\r\n" );
document.write( "    7b^2 + 34b + 26 = 0                             <<<---===  INMCORRECT REDUCTION.\r\n" );
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document.write( "But this reduction to the quadratic equation is INCORRECT.\r<BR>\n" );
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document.write( "Coefficients of this equation are NOT symmetric; therefore, this method of reduction <BR>\n" );
document.write( "to quadratic equation is INCORRECT.\r<BR>\n" );
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document.write( "Everything what follows in the post by @CPhill, is IRRELEVANT AND INCORRECT.\r<BR>\n" );
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document.write( "<H3>This \"solution\" from @CPhill is the total, global and fatal deception of a reader.</H3>\r<BR>\n" );
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document.write( "   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;THE &nbsp;PROBLEM &nbsp;IS &nbsp;NOT &nbsp;SOLVED.\r<BR>\n" );
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document.write( "////////////////////////////////////\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Regarding the post by @CPhill . . . \r<BR>\n" );
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document.write( "Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.\r<BR>\n" );
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document.write( "The artificial intelligence is like a baby now. It is in the experimental stage <BR>\n" );
document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It has no feeling of shame - it is shameless.\r<BR>\n" );
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document.write( "This time, again, &nbsp;it made an error.\r<BR>\n" );
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document.write( "Although the @CPhill' solution are copy-paste &nbsp;Google &nbsp;AI solutions, &nbsp;there is one essential difference.\r<BR>\n" );
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document.write( "Every time, &nbsp;Google &nbsp;AI &nbsp;makes a note at the end of its solutions that &nbsp;Google &nbsp;AI &nbsp;is experimental<BR>\n" );
document.write( "and can make errors/mistakes.\r<BR>\n" );
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document.write( "All @CPhill' solutions are copy-paste of &nbsp;Google &nbsp;AI &nbsp;solutions, with one difference:<BR>\n" );
document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.<BR>\n" );
document.write( "So, he NEVER SAYS TRUTH.\r<BR>\n" );
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document.write( "Every time, &nbsp;@CPhill embarrassed to tell the truth.\r<BR>\n" );
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document.write( "But I am not embarrassing to tell the truth, &nbsp;as it is my duty at this forum.\r<BR>\n" );
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document.write( "And the last my comment.\r<BR>\n" );
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document.write( "When you obtain such posts from @CPhill, &nbsp;remember, &nbsp;that &nbsp;NOBODY &nbsp;is responsible for their correctness, <BR>\n" );
document.write( "until the specialists and experts will check and confirm their correctness.\r<BR>\n" );
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document.write( "Without it, &nbsp;their reliability is &nbsp;ZERO and their creadability is &nbsp;ZERO, &nbsp;too.\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How to solve this problem.\r<BR>\n" );
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document.write( "Reduce the given polynomial to the standard form.\r<BR>\n" );
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document.write( "This polynomial has no rational roots that can be found using Rational Root Test.\r<BR>\n" );
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document.write( "At this point, there are 3 ways to follow.\r<BR>\n" );
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document.write( "First way is to use formula for quartic polynomial equation.<BR>\n" );
document.write( "This way is not practical and it is never used in school Math assignments.\r<BR>\n" );
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document.write( "Second way is to use online solvers, for example, at this site<BR>\n" );
document.write( "https://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php<BR>\n" );
document.write( "They will provide all real and complex roots.\r<BR>\n" );
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document.write( "Third way is to use graphic calculator or an appropriate plotting tools,<BR>\n" );
document.write( "for example, at this site (free of charge)<BR>\n" );
document.write( "www.desmos.com/calculator<BR>\n" );
document.write( "It will provide real roots.\r<BR>\n" );
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document.write( "Have a nice day!\r<BR>\n" );
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document.write( "<H2>Obtaining such \"solutions\" from @CPhill, <BR>\n" );
document.write( "I would not trust to any his word and/or number.<H2><H3>The computer program, which uses this \"Artificial intelligence,\"<BR>\n" );
document.write( "works based on the principle \"to deceive a reader at any cost\".<H3>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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