document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944520>Question 944520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum ot two numbers is 6 and their product is 7. What is the sum of their cubes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575906 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=575906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+y = 6<BR>\n" );
document.write( "xy = 7\r<BR>\n" );
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document.write( "Using sum of cubes,<BR>\n" );
document.write( "x^3 + y^3 = (x+y)(x^2 - xy + y^2) = 6(x^2 + y^2 - 7)\r<BR>\n" );
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document.write( "To find x^2 + y^2, we have (x+y)^2 = 36 = x^2 + y^2 + 2xy = x^2 + y^2 + 2*7, so x^2 + y^2 = 36 - 14 = 22.\r<BR>\n" );
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document.write( "Then x^3 + y^3 = 6(22 - 7) = 90.\r<BR>\n" );
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document.write( "An alternate solution is to solve the quadratic x^2 - 6x + 7 for both its roots, obtaining 3 + sqrt(2) and 3 - sqrt(2), cubing and summing also gives 90. </SPAN>\n" );
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