document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079386>Question 1079386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a+b=3 and a^3+b^3=6, given the formula (a+b)^3 = a^3+3a^2b+3ab^2+b^3, find the value of ab. Hence, find the value of a^2+b^2.\r<BR>\n" );
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document.write( "All I figured out was that a^2-ab+b^2=2\r<BR>\n" );
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document.write( "Thank you honestly so much for your time and effort! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693693 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=693693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: a+b=3, a^3+b^3=6<BR>\n" );
document.write( "(a+b)^3 = a^3+3a^2b+3ab^2+b^3<BR>\n" );
document.write( "Since a^3+b^3=6 and a+b=3, we have<BR>\n" );
document.write( "3^3 = 6 + 3a^2b + 3ab^2<BR>\n" );
document.write( "21 = 3a^2b + 3ab^2<BR>\n" );
document.write( "Pulling out the common factor 3ab, we get<BR>\n" );
document.write( "21 = 3ab(a+b) = 3*3*ab<BR>\n" );
document.write( "Thus ab = 21/9 = 7/3<BR>\n" );
document.write( "(a+b)^2 = a^2+b^2+2ab<BR>\n" );
document.write( "Subtract 2ab from both sides:<BR>\n" );
document.write( "(a+b)^2 - 2ab = a^2 + b^2<BR>\n" );
document.write( "3^2 - 2(7/3) = a^2 + b^2<BR>\n" );
document.write( "9 - 14/3 = (27-14)/3 = 13/3<BR>\n" );
document.write( "So a^2 + b^2 = 13/3 </SPAN>\n" );
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