document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658834>Question 658834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2+y^2=48<BR>\n" );
document.write( "(x-y)=4<BR>\n" );
document.write( "Find the value of xy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410491 by </B><A HREF=/tutors/aboutme.mpl?userid=kevwill><B>kevwill(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kevwill><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=kevwill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+=+4 ALIGN=MIDDLE  ALT=\"x+-+y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > we know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x-4 ALIGN=MIDDLE  ALT=\"y+=+x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into the first equation gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x-4%29%5E2+=+48 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x-4%29%5E2+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Expanding:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x%5E2+-+8x+%2B+16+=+48 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%5E2+-+8x+%2B+16+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combining like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+8x+%2B+16+=+48 ALIGN=MIDDLE  ALT=\"2x%5E2+-+8x+%2B+16+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 48 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+8x+-+32+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+8x+-+32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+-+16+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+-+16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This can be solved using the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a=1, b=-4, and c=-16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A%28-16%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A%28-16%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+16%2B64+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16%2B64+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+80+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+80+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+16%2A5+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16%2A5+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+4%2Asqrt%28+5+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+4%2Asqrt%28+5+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2+%2B-+2%2Asqrt%28+5+%29+ ALIGN=MIDDLE  ALT=\"x+=+2+%2B-+2%2Asqrt%28+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So x can have the values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2B2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=2%2B2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2-2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=2-2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2B2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+2%2B2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x-4+=+-2%2B2%2Asqrt%285%29-2 ALIGN=MIDDLE  ALT=\"y+=+x-4+=+-2%2B2%2Asqrt%285%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+%282%2B2%2Asqrt%285%29%29%282%2Asqrt%285%29-2%29+=+4%2Asqrt%285%29+-+4+%2B+20+-+4%2Asqrt%285%29+=+16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Checking:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+%282+%2B+2%2Asqrt%285%29%29%5E2+%2B+%28-2+%2B+2%2Asqrt%285%29-2%29%5E2+=+%284+%2B+8%2Asqrt%285%29%2B20%29+%2B+%284+-+8%2Asqrt%285%29+%2B+20%29+=+4%2B20%2B20%2B4+%2B+8%2Asqrt%285%29+-+8%2Asqrt%285%29+=+48 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+%282-2%2Asqrt%285%29%29%28-2-2%2Asqrt%285%29%29+=+-4+-+4%2Asqrt%285%29+%2B+4%2Asqrt%285%29+%2B+20+=+16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2-2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+2-2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x-4+=+-2-2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"y+=+x-4+=+-2-2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Checking:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+%282+-+2%2Asqrt%285%29%29%5E2+%2B+%28-2+-+2%2Asqrt%285%29-2%29%5E2+=+%284+-+8%2Asqrt%285%29%2B20%29+%2B+%284+%2B+8%2Asqrt%285%29+%2B+20%29+=+4%2B20%2B4%2B20+-+8%2Asqrt%285%29+%2B+8%2Asqrt%285%29+=+48 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+%282-2%2Asqrt%285%29%29%28-2-2%2Asqrt%285%29%29+=+-4+-+4%2Asqrt%285%29+%2B+4%2Asqrt%285%29+%2B+20+=+16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So for either value of x, x*y = 16<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );