document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177379>Question 1177379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a%5E2+%2B+4b%5E2+%2B+c%5E2+=+4ab+%2B+2ac+ ALIGN=MIDDLE  ALT=\"+2a%5E2+%2B+4b%5E2+%2B+c%5E2+=+4ab+%2B+2ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Find the value of cosB.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806327 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a%5E2+%2B+4b%5E2+%2B+c%5E2+=+4ab+%2B+2ac+ ALIGN=MIDDLE  ALT=\"+2a%5E2+%2B+4b%5E2+%2B+c%5E2+=+4ab+%2B+2ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2+%2B+a%5E2+%2B4b%5E2+%2B+c%5E2+-+4ab+-+2ac=0+ ALIGN=MIDDLE  ALT=\"+a%5E2+%2B+a%5E2+%2B4b%5E2+%2B+c%5E2+-+4ab+-+2ac=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-2ac+%2Bc%5E2+%2Ba%5E2+-4ab%2B4b%5E2=0 ALIGN=MIDDLE  ALT=\"a%5E2+-2ac+%2Bc%5E2+%2Ba%5E2+-4ab%2B4b%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-c%29%5E2+%2B%28a-2b%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28a-c%29%5E2+%2B%28a-2b%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here a, b and c are positive real numbers, and if (a - 2b)^2 > 0, then (a - c)^2  is positive so a - 2b = 0 and a - c = 0.<BR>\n" );
document.write( "a - 2b = a - c<BR>\n" );
document.write( "c = 2b<BR>\n" );
document.write( "Plug in the original equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2+%2B+4b%5E2+%2B+4b%5E2 ALIGN=MIDDLE  ALT=\"2a%5E2+%2B+4b%5E2+%2B+4b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 2a^2 + 8b^2<BR>\n" );
document.write( "= 4ab + 4ab<BR>\n" );
document.write( "= 8ab<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2a%5E2+-+8ab+%2B+8b%5E2 ALIGN=MIDDLE  ALT=\"0+=+2a%5E2+-+8ab+%2B+8b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+a%5E2+-+4ab+%2B+4b%5E2 ALIGN=MIDDLE  ALT=\"0=+a%5E2+-+4ab+%2B+4b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= (a - 2b)^2<BR>\n" );
document.write( "a - 2b = 0<BR>\n" );
document.write( "a = 2b<BR>\n" );
document.write( "Plug in original equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8b%5E2+%2B+4b%5E2+%2B+4b%5E2+=+4a%28a%2F2%29+%2B+2c%28c%29 ALIGN=MIDDLE  ALT=\"8b%5E2+%2B+4b%5E2+%2B+4b%5E2+=+4a%28a%2F2%29+%2B+2c%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2+%2B+2c%5E2 ALIGN=MIDDLE  ALT=\"2a%5E2+%2B+2c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16b%5E2 ALIGN=MIDDLE  ALT=\"16b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=+%281%2F8%29+a%5E2+%2B+%281%2F8%29+c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=+%281%2F8%29+a%5E2+%2B+%281%2F8%29+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+c%5E2+-+%28%287%2F8%29+a%5E2+%2B+%287%2F8%29+c%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+c%5E2+-+%28%287%2F8%29+a%5E2+%2B+%287%2F8%29+c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using Law of Cosines,<BR>\n" );
document.write( "2accos(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F8%29+a%5E2+%2B+%287%2F8%29+c%5E2 ALIGN=MIDDLE  ALT=\"%287%2F8%29+a%5E2+%2B+%287%2F8%29+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 8<BR>\n" );
document.write( "16ac *cos(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2+%2B+7c%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2+%2B+7c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cos(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a%5E2+%2B+7c%5E2%29%2F%2816ac%29 ALIGN=MIDDLE  ALT=\"%287a%5E2+%2B+7c%5E2%29%2F%2816ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%284b%5E2%29+%2B+7%284b%5E2%29%29%2F%2816%284b%5E2%29%29 ALIGN=MIDDLE  ALT=\"+%287%284b%5E2%29+%2B+7%284b%5E2%29%29%2F%2816%284b%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2856b%5E2%29%2F%2864b%5E2%29 ALIGN=MIDDLE  ALT=\"%2856b%5E2%29%2F%2864b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 56/64<BR>\n" );
document.write( "= 7/8<BR>\n" );
document.write( "Hence cos(B) = 7/8. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );