document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564841>Question 564841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference of two positive numbers is 4 and the sum of their squares is 40. Find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365505 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=365505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers = a and b<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "a - b = 4 -> a = b + 4<BR>\n" );
document.write( "a^2 + b^2 = 40<BR>\n" );
document.write( "(b+4)^2 + b^2 = 40<BR>\n" );
document.write( "Solve for b:<BR>\n" );
document.write( "b^2 + 8b + 16 + b^2 - 40 = 0<BR>\n" );
document.write( "2(b^2 + 4b - 12) = 0<BR>\n" );
document.write( "Factoring gives<BR>\n" );
document.write( "(b-2)(b+6) = 0<BR>\n" );
document.write( "Since the numbers are positive, we have b=2<BR>\n" );
document.write( "Therefore the two numbers are 2 and 6 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );