document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209558>Question 1209558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) If 7^sin²x - 7^cos²x = 8<BR>\n" );
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document.write( "b) Let m be a given real number, Find all complex numbers x such that,<BR>\n" );
document.write( "([x/(x+1)]² + [x/(x-1)]² = m² + m\r<BR>\n" );
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document.write( "c) ab = ½, bc = ⅓, ac = 1/6,<BR>\n" );
document.write( "find (1/a²) + (1/b²) + (1/c²)\r<BR>\n" );
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document.write( "d) 2^x - 3^y = 5<BR>\n" );
document.write( "2^(x+2) + 3^(y+2) = 59. <BR>\n" );
document.write( "find xy\r<BR>\n" );
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document.write( "e) find m, <BR>\n" );
document.write( "9^4^m = 4^9^m\r<BR>\n" );
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document.write( "f) (7^log₈x)×(x^log₉x) = 3969, <BR>\n" );
document.write( "find x.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849524 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=849524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Part &nbsp;(a)</U>\r<BR>\n" );
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document.write( "Let's consider part &nbsp;(a) &nbsp;first, &nbsp;with equation \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7^(sin^2(x)) - 7^(cos^2(x)) = 8.\r<BR>\n" );
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document.write( "Due to &nbsp;OBVIOUS &nbsp;reasons, &nbsp;this equation has no real solutions.\r<BR>\n" );
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document.write( "Indeed, &nbsp;sin^2(x) &nbsp;has the maximum value of &nbsp;1;  &nbsp;hence,  &nbsp;7^(sin^2(x)) &nbsp;has maximum value of 7.\r<BR>\n" );
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document.write( "Next, &nbsp;from &nbsp;7^(sin^2(x)), &nbsp;the equation subtracts &nbsp;7^(cos^2(x)), &nbsp;which is non-negative<BR>\n" );
document.write( "real number, &nbsp;so the left side of the equation &nbsp;CAN &nbsp;NOT &nbsp;be greater than &nbsp;7.\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A fortiori, &nbsp;it can not be &nbsp;8.\r<BR>\n" );
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document.write( "At this point, &nbsp;my solution is complete, and the \r<BR>\n" );
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document.write( "<U>ANSWER</U> &nbsp;&nbsp;is: &nbsp;&nbsp;this given equation has no solution/solutions in real numbers.\r<BR>\n" );
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document.write( "The solution by the &nbsp;@CPhill to this problem has a &nbsp;FATAL &nbsp;ERROR:\r<BR>\n" );
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document.write( "it incorrectly factors &nbsp;&nbsp;y^2 - 8y - 7 = 0  &nbsp;as  &nbsp;&nbsp;(y-7)*(y+1) = 0,\r<BR>\n" );
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document.write( "which leads him to further wrong conclusions.\r<BR>\n" );
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document.write( "This example/case tells me that @CPhill \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- does not look at his solutions;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- does not read his solutions;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- does not check them;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- does not think about them;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- does not care about the correctness of his solutions,\r<BR>\n" );
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document.write( "and, &nbsp;in general, &nbsp;does not understand, &nbsp;what he is doing and what he posts <BR>\n" );
document.write( "to this forum, in particular, and to the outer world, &nbsp;in general.\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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Part &nbsp;(c)</U>  \r<BR>\n" );
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document.write( "In the post by &nbsp;@CPhill, &nbsp;the solution for part &nbsp;(c) &nbsp;is &nbsp;INCORRECT.\r<BR>\n" );
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document.write( "The correct solution is given at this forum under this link\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209563.html\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In future, do not pack more than one problem per post.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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