document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848415>Question 848415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two numbers have the sum of one and a sum of cubes 31. what is the product? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511068 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  two numbers have the sum of one<BR>\n" );
document.write( "a + b = 1<BR>\n" );
document.write( "a = (1-b)<BR>\n" );
document.write( "and a sum of cubes 31.<BR>\n" );
document.write( "a^3 + b^3 = 31<BR>\n" );
document.write( "replace a with (1-b)<BR>\n" );
document.write( "(1-b)^3 + b^3 = 31<BR>\n" );
document.write( "FOIL (1-b)(1-b)(1-b) = 1 - 3b + 3b^2 - b^3<BR>\n" );
document.write( "1 - 3b + 3b^2 - b^3 + b^3 = 31<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "3b^2 - 3b + 1 - 31 = 0<BR>\n" );
document.write( "3b^2 - 3b - 30 = 0<BR>\n" );
document.write( "using the quadratic formula, I got:<BR>\n" );
document.write( "b = -2.70156212 then a = 3.70156212<BR>\n" );
document.write( "or<BR>\n" );
document.write( "b = 3.70156212 then a = -2.70156212<BR>\n" );
document.write( ":<BR>\n" );
document.write( "what is the product?<BR>\n" );
document.write( "-2.70156212 * 3.70156212 = -10 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );