document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204480>Question 1204480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 4/3 ,M, 1, N is form GP, what is the product of M and N  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840756 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Tutor @josgarithmetic has the right answer immediately... but in trying to check her result she does some sloppy algebra, arriving at a contradiction.<br><BR>\n" );
document.write( "In a geometric progression, the square of any term is equal to the product of the two terms on either side of it.  Using that fact, we get the answer immediately:<br><BR>\n" );
document.write( "1^2 = (M)(N)<BR>\n" );
document.write( "MN = 1<br><BR>\n" );
document.write( "ANSWER: MN = 1<br><BR>\n" );
document.write( "The problem doesn't ask us to find M and N; but we can easily.<br><BR>\n" );
document.write( "M^2 = (4/3)(1)<BR>\n" );
document.write( "M^2 = 4/3<BR>\n" );
document.write( "M = 2/sqrt(3)<br><BR>\n" );
document.write( "That gives us sqrt(3)/2 as the common ratio; and that gives us N = sqrt(3)/2.<br><BR>\n" );
document.write( "The terms of the GP are 4/3, M=2/sqrt(3), 1, and N=sqrt(3)/2.<br><BR>\n" );
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