document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209768>Question 1209768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a = sin50(1 + 2cos170°), <BR>\n" );
document.write( "b = sin170°(1 + 2cos140°), <BR>\n" );
document.write( "c = sin140°(1 + 2cos50°), <BR>\n" );
document.write( "then (3 - 2A)ˣ = (x + 1)², <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 #850319 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</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=850319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "If a = sin50(1 + 2cos170°), <BR>\n" );
document.write( "b = sin170°(1 + 2cos140°), <BR>\n" );
document.write( "c = sin140°(1 + 2cos50°), <BR>\n" );
document.write( "then (3 - 2A)ˣ = (x + 1)², <BR>\n" );
document.write( "find x<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Regarding this problem, &nbsp;I have two notices.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One notice is that quantity &nbsp;A &nbsp;is never defined in the posted problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "@CPhill, &nbsp;without any explanations, &nbsp;uses  &nbsp;&nbsp;A = a + b + c, &nbsp;by an arbitrary way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "May be, &nbsp;it is correct, &nbsp;but it deserves a separate mentioning.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, @CPhill reduces the problem to equation \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%29%5Ex ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+1)^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "He obtained &nbsp;x = 0 &nbsp;as one of solutions.  &nbsp;&nbsp;It is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But he missed another solution, &nbsp;which does exist. &nbsp;&nbsp;It is &nbsp;x= -1.63775  &nbsp;&nbsp;(approximate).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It can be found graphically.  &nbsp;&nbsp;See the plot under this link\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.desmos.com/calculator/0s5w2nkiua\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This plot is produced by free of charge online plotting tool  www.desmos.com/calculator\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To get &nbsp;x-coordinate of the intersection point, &nbsp;click at this point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "///////////////////////////\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<U>Comment from student</U>: &nbsp;&nbsp;I made a mistake and I resent the complete question that &nbsp;&nbsp;A = a + b + c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<U>My response</U>: &nbsp;&nbsp;I expected to get from you something like \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;\"Thank you for your solution and for your teaching\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These are &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28FIRST%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28FIRST%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28WORDS%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28WORDS%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;you should pronounce when you communicate with a  tutor.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Did your mother or father or other relatives taught you how to communicate with other people outside ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );