document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461595>Question 461595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a,b,c,d > 0 and abcd=1, prove that (1+a)(1+b)(1+c)(1+d) >= 2^4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316663 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First up, let S = (1+a)(1 + b)(1 + c)(1 + d) = 1+c + d + cd + b + bc + bd + bcd + a + ac + ad + acd + ab + abc + abd + abcd.  (This expression has 16 terms.)<BR>\n" );
document.write( "By the AM-GM inequality, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2F16+%3E=+root%2816%2C+cdcdbbcbdbcdaacadacdababcabdabcd%29+=+root%2816%2C+a%5E8b%5E8c%5E8d%5E8%29+=+root%2816%2C+%28abcd%29%5E8%29+=+root%2816%2C1%29+=+1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,  since abcd = 1.\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+%3E=+16+=+2%5E4 ALIGN=MIDDLE  ALT=\"S+%3E=+16+=+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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