document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209471>Question 1209471</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%282sqrt%2810%29%2B11%29=x%2Bsqrt%28x%2By%29 ALIGN=MIDDLE  ALT=\"sqrt%282sqrt%2810%29%2B11%29=x%2Bsqrt%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find x-y.<BR>\n" );
document.write( "CC13F #6<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848912 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=848912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Consider the general expression<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Bsqrt%28b%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Bsqrt%28b%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Expanding this, we get<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2sqrt%28ab%29%2Bb ALIGN=MIDDLE  ALT=\"a%2B2sqrt%28ab%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%2B2sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2B2sqrt%28ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Turning this around, we have the general result<br><BR>\n" );
document.write( "[*] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28a%2Bb%29%2B2sqrt%28ab%29%29=sqrt%28a%29%2Bsqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28a%2Bb%29%2B2sqrt%28ab%29%29=sqrt%28a%29%2Bsqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In this problem, we have the expression<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%2B2sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%2B2sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Comparing that to the general result[*], we can see by inspection that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%2B2sqrt%2810%29%29=sqrt%281%29%2Bsqrt%2810%29=1%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%2B2sqrt%2810%29%29=sqrt%281%29%2Bsqrt%2810%29=1%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The problem asks us to write that in the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bsqrt%28x%2By%29 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So we want to have<br><BR>\n" );
document.write( "x = 1  and x+y = 10<br><BR>\n" );
document.write( "which leads us immediately to<br><BR>\n" );
document.write( "x = 1 and y = 9.<br><BR>\n" );
document.write( "Finally, the question asks for the value of x-y.<br><BR>\n" );
document.write( "ANSWER: x-y = 1-9 = -8<br>\r<BR>\n" );
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