document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023321>Question 1023321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rational numbers a and b given that<BR>\n" );
document.write( "a-2b + sqr(a+b) = sqr(6)/2\r<BR>\n" );
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document.write( "I really appreciate any help! Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638825 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=638825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5B1%5D=sqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"I%5B1%5D=sqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an irrational number,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-2b%2Bsqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a-2b%2Bsqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be irrational too.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > are rational,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=a-2b ALIGN=MIDDLE  ALT=\"R=a-2b\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be rational.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-2b%2Bsqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a-2b%2Bsqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is irrational, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=a-2b ALIGN=MIDDLE  ALT=\"R=a-2b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is rational,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5B2%5D=sqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"I%5B2%5D=sqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be irrational.<BR>\n" );
document.write( "What we have in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-2b%2Bsqrt%28a%2Bb%29=sqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"a-2b%2Bsqrt%28a%2Bb%29=sqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2BI%5B2%5D=I%5B1%5D ALIGN=MIDDLE  ALT=\"R%2BI%5B2%5D=I%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The only way that can be possible is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28R=0%2CI%5B2%5D=I%5B1%5D%29 ALIGN=MIDDLE  ALT=\"system%28R=0%2CI%5B2%5D=I%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a-2b=0%2Csqrt%28a%2Bb%29=sqrt%286%29%2F2%29 ALIGN=MIDDLE  ALT=\"system%28a-2b=0%2Csqrt%28a%2Bb%29=sqrt%286%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=2b%2Ca%2Bb=6%2F4%29 ALIGN=MIDDLE  ALT=\"system%28a=2b%2Ca%2Bb=6%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=2b%2C2b%2Bb=3%2F2%29 ALIGN=MIDDLE  ALT=\"system%28a=2b%2C2b%2Bb=3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=2b%2C3b=3%2F2%29 ALIGN=MIDDLE  ALT=\"system%28a=2b%2C3b=3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=2b%2Cb=1%2F2%29 ALIGN=MIDDLE  ALT=\"system%28a=2b%2Cb=1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28a=1%2Cb=1%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28a=1%2Cb=1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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