document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478287>Question 478287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the positive integers is 8 and the sum of their cubes is 152. what is the product of the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327700 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=327700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the positive integers is 8 and the sum of their cubes is 152. what is the product of the two numbers?<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "x + y = 8<BR>\n" );
document.write( "x^3+y^3 = 152<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Divide 1st into 2nd to get:<BR>\n" );
document.write( "x^2-xy+y^2 = 19<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute for \"x\" and solve for \"y\":<BR>\n" );
document.write( "(8-y)^2 - (8-y)y + y^2 = 19<BR>\n" );
document.write( "64 -16y+y^2-8y+y^2 + y^2 = 19<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3y^2 - 24y + 45 = 0<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "y^2 - 8y + 15 = 0<BR>\n" );
document.write( "(y-3)(y-5)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If y = 3, x = 5<BR>\n" );
document.write( "If y = 5, x = 3<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );