document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878746>Question 878746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For  a= Sqrt(10)+ sqrt(2)/2   and  b=  Sqrt(10)- sqrt(2)/2   , we have <BR>\n" );
document.write( "Log2 (a^2+ab+b^2)= ?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530410 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=530410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28a%5E2%2Bab%2Bb%5E2%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28a%5E2%2Bab%2Bb%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? That looks like a lot of calculation work, no matter how creatively you try to do it.<BR>\n" );
document.write( " <BR>\n" );
document.write( "DIVIDE AND CONQUER:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab%2Bb%5E2=la%5E2%2B2ab%2Bb%5E2-ab=%28a%2Bb%29%5E2-ab ALIGN=MIDDLE  ALT=\"a%5E2%2Bab%2Bb%5E2=la%5E2%2B2ab%2Bb%5E2-ab=%28a%2Bb%29%5E2-ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab=%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%28sqrt%2810%29-sqrt%282%29%2F2%29=%28sqrt%2810%29%29%5E2-%28sqrt%282%29%2F2%29%5E3=10-1%2F2=19%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%2B%28sqrt%2810%29-sqrt%282%29%2F2%29=sqrt%2810%29%2Bsqrt%282%29%2F2%2Bsqrt%2810%29-sqrt%282%29%2F2=2sqrt%2810%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=%282sqrt%2810%29%29%5E2=2%5E2%28sqrt%2810%29%29%5E2=4%2A10=40 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=%282sqrt%2810%29%29%5E2=2%5E2%28sqrt%2810%29%29%5E2=4%2A10=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab%2Bb%5E2=%28a%2Bb%29%5E2-ab=40-19%2F2=80%2F2-19%2F2=61%2F2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab%2Bb%5E2=%28a%2Bb%29%5E2-ab=40-19%2F2=80%2F2-19%2F2=61%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28a%5E2%2Bab%2Bb%5E2%29%29=log%282%2C%2861%2F2%29%29=log%282%2C61%29-log%282%2C2%29=highlight%28log%282%2C61%29-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "An approximate value can be calculated (by a calculator) or using a table of logaritms) as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C61%29-1=log%2861%29%2Flog%282%29-1 ALIGN=MIDDLE  ALT=\"log%282%2C61%29-1=log%2861%29%2Flog%282%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=approx<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.78533%2F0.30103=about5.93-1=about4.93 ALIGN=MIDDLE  ALT=\"1.78533%2F0.30103=about5.93-1=about4.93\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "GRIT YOUR TEETH AND GO:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28a%5E2%2Bab%2Bb%5E2%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28a%5E2%2Bab%2Bb%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=log%282%2C%28%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%5E2%2B%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%28sqrt%2810%29-sqrt%282%29%2F2%29%2B%28sqrt%2810%29-sqrt%282%29%2F2%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%5E2%2B%2810-1%2F2%29%2B%28sqrt%2810%29-sqrt%282%29%2F2%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%28%28sqrt%2810%29%29%5E2%2B2sqrt%2810%29%28sqrt%282%29%2F2%29%2B%28sqrt%282%29%2F2%29%5E2%29%2B19%2F2%2B%28%28sqrt%2810%29%29%5E2-2sqrt%2810%29%28sqrt%282%29%2F2%29%2B%28sqrt%282%29%2F2%29%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%2810%2B2sqrt%2810%29%28sqrt%282%29%2F2%29%2B1%2F2%29%2B19%2F2%2B%2810-2sqrt%2810%29%28sqrt%282%29%2F2%29%2B1%2F2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%2810%2B2sqrt%2810%29%28sqrt%282%29%2F2%29%2B1%2F2%2B19%2F2%2B10-2sqrt%2810%29%28sqrt%282%29%2F2%29%2B1%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%2820%2B1%2B19%2F2%29%29=log%282%2C%2842%2F2%2B19%2F2%29%29=log%282%2C%2861%2F2%29%29=log%282%2C61%29-log%282%2C2%29=log%282%2C61%29-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <BR>\n" );
document.write( "A CREATIVE IDEA THAT DID NOT WORK TOO WELL:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives me an idea:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab%2Bb%5E2=%28a%5E3-b%5E3%29%2F%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab%2Bb%5E2=%28a%5E3-b%5E3%29%2F%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b=%28sqrt%2810%29%2Bsqrt%282%29%2F2%29-%28sqrt%2810%29-sqrt%282%29%2F2%29=sqrt%2810%29%2Bsqrt%282%29%2F2-sqrt%2810%29%2Bsqrt%282%29%2F2=sqrt%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-b%5E3=%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%5E3-%28sqrt%2810%29-sqrt%282%29%2F2%29%5E3 ALIGN=MIDDLE  ALT=\"a%5E3-b%5E3=%28sqrt%2810%29%2Bsqrt%282%29%2F2%29%5E3-%28sqrt%2810%29-sqrt%282%29%2F2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5B%22 ALIGN=MIDDLE  ALT=\"%22%5B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%29%5E3%2B3%28sqrt%2810%29%29%5E2%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%28sqrt%282%29%2F2%29%5E2%2B%28sqrt%282%29%2F2%29%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5D+-+%5B%22 ALIGN=MIDDLE  ALT=\"%22%5D+-+%5B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%29%5E3-3%28sqrt%2810%29%29%5E2%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%28sqrt%282%29%2F2%29%5E2-%28sqrt%282%29%2F2%29%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5D%22 ALIGN=MIDDLE  ALT=\"%22%5D%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5B%22 ALIGN=MIDDLE  ALT=\"%22%5B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%2810%29%2B3%2810%29%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%281%2F2%29%2Bsqrt%282%29%2F4 ALIGN=MIDDLE  ALT=\"10sqrt%2810%29%2B3%2810%29%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%281%2F2%29%2Bsqrt%282%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5D+-+%5B%22 ALIGN=MIDDLE  ALT=\"%22%5D+-+%5B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%2810%29-3%2810%29%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%281%2F2%29-sqrt%282%29%2F4 ALIGN=MIDDLE  ALT=\"10sqrt%2810%29-3%2810%29%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%281%2F2%29-sqrt%282%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%5D%22 ALIGN=MIDDLE  ALT=\"%22%5D%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%2810%29%2B3%2A%2810%29%2A%28sqrt%282%29%2F2%29%2B3sqrt%2810%29%281%2F2%29%2Bsqrt%282%29%2F4-10sqrt%2810%29%2B3%2810%29%28sqrt%282%29%2F2%29-3sqrt%2810%29%281%2F2%29%2Bsqrt%282%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%2810%29%2A%28sqrt%282%29%2F2%29%2Bsqrt%282%29%2F4%2B3%2A%2810%29%2A%28sqrt%282%29%2F2%29%2Bsqrt%282%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30sqrt%282%29%2F2%2Bsqrt%282%29%2F4%2B30sqrt%282%29%2F2%2Bsqrt%282%29%2F4 ALIGN=MIDDLE  ALT=\"30sqrt%282%29%2F2%2Bsqrt%282%29%2F4%2B30sqrt%282%29%2F2%2Bsqrt%282%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30sqrt%282%29%2F2%2B30sqrt%282%29%2F2%2Bsqrt%282%29%2F2=%2860sqrt%282%29%2Bsqrt%282%29%29%2F2=61sqrt%282%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab%2Bb%5E2=%28a%5E3-b%5E3%29%2F%28a%2Bb%29=%2861sqrt%282%29%2F2%29%2Fsqrt%282%29=61%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28a%5E2%2Bab%2Bb%5E2%29%29=log%282%2C%2861%2F2%29%29=log%282%2C61%29-log%282%2C2%29=log%282%2C61%29-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );