document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140916>Question 1140916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, my question is: <BR>\n" );
document.write( "If x>y>z then prove xy + yz > (x+y)(y+z) / 2\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761575 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=761575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3Ey%3Ez ALIGN=MIDDLE  ALT=\"x%3Ey%3Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%3E0 ALIGN=MIDDLE  ALT=\"x-y%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-z%3E0 ALIGN=MIDDLE  ALT=\"y-z%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%28y-z%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-y%29%28y-z%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-xz-y%5E2%2Byz%3E0 ALIGN=MIDDLE  ALT=\"xy-xz-y%5E2%2Byz%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2Byz-xz-y%5E2%3E0 ALIGN=MIDDLE  ALT=\"xy%2Byz-xz-y%5E2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B2yz-xy-yz-xz-y%5E2%3E0 ALIGN=MIDDLE  ALT=\"2xy%2B2yz-xy-yz-xz-y%5E2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B2yz-%28xy%2Byz%2Bxz%2By%5E2%29%3E0 ALIGN=MIDDLE  ALT=\"2xy%2B2yz-%28xy%2Byz%2Bxz%2By%5E2%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28xy%2Byz%29-%28x%2By%29%28y%2Bz%29%3E0 ALIGN=MIDDLE  ALT=\"2%28xy%2Byz%29-%28x%2By%29%28y%2Bz%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy%2Byz%29-%28x%2By%29%28y%2Bz%29%2F2%3E0 ALIGN=MIDDLE  ALT=\"%28xy%2Byz%29-%28x%2By%29%28y%2Bz%29%2F2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28xy%2Byz%3E%28x%2By%29%28y%2Bz%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28xy%2Byz%3E%28x%2By%29%28y%2Bz%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "How did I come up with that?<BR>\n" );
document.write( "Starting from the end and working backwards to the beginning<BR>\n" );
document.write( "from one equivalent equation to another: <BR>\n" );
document.write( "If and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+%2B+yz+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E0 ALIGN=MIDDLE  ALT=\"xy+%2B+yz+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+xy+%2B+yz+%3E+%28x%2By%29%28y%2Bz%29+%2F+2 ALIGN=MIDDLE  ALT=\"+xy+%2B+yz+%3E+%28x%2By%29%28y%2Bz%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The two equations are equivalent;<BR>\n" );
document.write( "it is the same statement said \"with other words\",<BR>\n" );
document.write( "so we just have to prove that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+%2B+yz+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"xy+%2B+yz+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy+%2B2yz%29%2F2+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"%282xy+%2B2yz%29%2F2+-+%28x%2By%29%28y%2Bz%29+%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy+%2B2yz-+%28x%2By%29%28y%2Bz%29%29%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"%282xy+%2B2yz-+%28x%2By%29%28y%2Bz%29%29%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy+%2B2yz-+%28xy%2Bxz%2By%5E2%2Byz%29%29%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"%282xy+%2B2yz-+%28xy%2Bxz%2By%5E2%2Byz%29%29%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy+%2B2yz-+xy-xz-y%5E2-yz%29%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"%282xy+%2B2yz-+xy-xz-y%5E2-yz%29%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy+%2Byz-xz-y%5E2%29%2F+2+%3E+0 ALIGN=MIDDLE  ALT=\"%28xy+%2Byz-xz-y%5E2%29%2F+2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+%2Byz-xz-y%5E2%3E+0 ALIGN=MIDDLE  ALT=\"xy+%2Byz-xz-y%5E2%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \"in other words\" that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-y%29%28y-x%29%3E0 ALIGN=MIDDLE  ALT=\"%28z-y%29%28y-x%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );