document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537214>Question 537214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers have a difference of 3.The sum of their square is 89.Find the number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352768 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two numbers have a difference of 3.The sum of their square is 89.<BR>\n" );
document.write( "Find the numbers.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Equatiions:<BR>\n" );
document.write( "x -y = 3<BR>\n" );
document.write( "x^2 + y^2 = 89<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = y + 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute and solve for \"y\":<BR>\n" );
document.write( "(y+3)^2 + y^2 = 89<BR>\n" );
document.write( "y^2+6y+9 + y^2 = 89<BR>\n" );
document.write( "----<BR>\n" );
document.write( "2y^2 + 6y -80 = 0<BR>\n" );
document.write( "y^2 + 3y - 40 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "y^2+8y-5y-40 = 0<BR>\n" );
document.write( "y(y+8)-5(y+8) = 0<BR>\n" );
document.write( "(y+8)(y-5)= 0 <BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 5 or y = -8<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve for \"x\":<BR>\n" );
document.write( "x-y = 3<BR>\n" );
document.write( "If x = 5, y = 2<BR>\n" );
document.write( "If x = -8, y = -11<BR>\n" );
document.write( "---------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Checking (5,2)<BR>\n" );
document.write( "x -y = 3<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + y^2 = 89<BR>\n" );
document.write( "5^2+2^2 = 89<BR>\n" );
document.write( "false<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Checking (-8,-11)<BR>\n" );
document.write( "x-y = 3<BR>\n" );
document.write( "-8--11 = 3<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2+y^2 = 89<BR>\n" );
document.write( "64+121 = 89<BR>\n" );
document.write( "false<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );