document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=775436>Question 775436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a,b,c are three distinct real numbers in geometric progression and a+b+c=xb then prove that x is greater than3 or less than -1<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 #472961 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=472961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The three numbers are in geometric progression, sp<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa=r ALIGN=MIDDLE  ALT=\"b%2Fa=r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b%2Fr ALIGN=MIDDLE  ALT=\"a=b%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fb=r ALIGN=MIDDLE  ALT=\"c%2Fb=r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=br ALIGN=MIDDLE  ALT=\"c=br\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common ratio of the progression.<BR>\n" );
document.write( "Since a,b,c are three distinct numbers,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C%3E1 ALIGN=MIDDLE  ALT=\"r%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C%3E-1 ALIGN=MIDDLE  ALT=\"r%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=b%2Fr%2Bb%2Bbr=%28b%2Bbr%2Bbr%5E2%29%2Fr=b%281%2Br%2Br%5E2%29%2Fr ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=b%2Fr%2Bb%2Bbr=%28b%2Bbr%2Bbr%5E2%29%2Fr=b%281%2Br%2Br%5E2%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=xb ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=xb\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xb=b%281%2Br%2Br%5E2%29%2Fr ALIGN=MIDDLE  ALT=\"xb=b%281%2Br%2Br%5E2%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Br%2Br%5E2%29%2Fr ALIGN=MIDDLE  ALT=\"x=%281%2Br%2Br%5E2%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C0 ALIGN=MIDDLE  ALT=\"r%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C%3E-1 ALIGN=MIDDLE  ALT=\"r%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=%281%2Br%2Br%5E2%29%2Fr%2B1=%281%2B2r%2Br%5E2%29%2Fr=%28r%2B1%29%5E2%2Fr%3C0 ALIGN=MIDDLE  ALT=\"x%2B1=%281%2Br%2Br%5E2%29%2Fr%2B1=%281%2B2r%2Br%5E2%29%2Fr=%28r%2B1%29%5E2%2Fr%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1%3C0 ALIGN=MIDDLE  ALT=\"x%2B1%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3C-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3C-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3E0 ALIGN=MIDDLE  ALT=\"r%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C%3E1 ALIGN=MIDDLE  ALT=\"r%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=%281%2Br%2Br%5E2%29%2Fr-3=%281-2r%2Br%5E2%29%2Fr=%28r-1%29%5E2%2Fr%3E0 ALIGN=MIDDLE  ALT=\"x-3=%281%2Br%2Br%5E2%29%2Fr-3=%281-2r%2Br%5E2%29%2Fr=%28r-1%29%5E2%2Fr%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%3E0 ALIGN=MIDDLE  ALT=\"x-3%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E3%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );