document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189763>Question 1189763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x and y are integers and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+2sqrt%28+10+%29+%2B+11+%29+=+x+%2B+sqrt%28+x+%2B+y+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+2sqrt%28+10+%29+%2B+11+%29+=+x+%2B+sqrt%28+x+%2B+y+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find x - y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821237 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Consider the general expansion<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bsqrt%28b%29%29%5E2=%28a%5E2%2Bb%29%2B2a%28sqrt%28b%29%29 ALIGN=MIDDLE  ALT=\"%28a%2Bsqrt%28b%29%29%5E2=%28a%5E2%2Bb%29%2B2a%28sqrt%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can use that pattern to attempt to find the value of an expression of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28m%2Bsqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28m%2Bsqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In this problem, the expression under the radical on the left is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2810%29%2B11 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2B2%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"11%2B2%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "According to the pattern above, we should have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb=11 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10 ALIGN=MIDDLE  ALT=\"b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "And those are all satisfied when a=1 and b=10.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%2B2%2Asqrt%2810%29%29+=+1%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%2B2%2Asqrt%2810%29%29+=+1%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Replacing the left side of the given equation with that gives us<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%2810%29=x%2Bsqrt%28x%2By%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%2810%29=x%2Bsqrt%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving by equating the rational and irrational parts of the two expressions gives us x=1 and y=9; so then<br><BR>\n" );
document.write( "ANSWER: x-y = -8<br><BR>\n" );
document.write( " </SPAN>\n" );
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