document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483278>Question 483278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find four numbers in GP whose sum is 85 and their product is 4096 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #330750 by </B><A HREF=/tutors/aboutme.mpl?userid=mathstutor494><B>mathstutor494(120)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathstutor494><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=mathstutor494><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=330750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the 4 numbers in GP be<BR>\n" );
document.write( "a/r, a, ar, ar^2\r<BR>\n" );
document.write( "\n" );
document.write( "Given that sum is 85 and their product is 4096. \r<BR>\n" );
document.write( "\n" );
document.write( "Accordingly....<BR>\n" );
document.write( "a/r+a+ar+ar^2=85 & a/r*a*ar*ar^2=4096<BR>\n" );
document.write( "a/r(1+r+r^2+r^3)=85 & a^4r^2 = 4096 \r<BR>\n" );
document.write( "\n" );
document.write( "Since a^4r^2 = 4096 so a^4= 4096/r^2 = 8^4/r^2<BR>\n" );
document.write( "So a = 8/sqrt(r)\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting value of a in sum equation leads to ...<BR>\n" );
document.write( "(8/sqrt(r)r)(1+r+r^2+r^3)=85<BR>\n" );
document.write( "(1+r+r^2+r^3)/(sqrt(r)r)= 85/8<BR>\n" );
document.write( "Therefore <BR>\n" );
document.write( "(1+r+r^2+r^3)= 85 and sqrt(r)r = 8<BR>\n" );
document.write( "Solving 2nd eqn<BR>\n" );
document.write( "r*r^(1/2)= 2^(3/2)<BR>\n" );
document.write( "r^(3/2)= 4^(3/2)<BR>\n" );
document.write( "so r = 4\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting value of r in below eqn and solving for a<BR>\n" );
document.write( "a^4r^2 = 4096 <BR>\n" );
document.write( "(a^4)(4^2)=4096 <BR>\n" );
document.write( "(a^4)*16= 4096 <BR>\n" );
document.write( "(a^4)= 4096/16 = 256 = 4^4<BR>\n" );
document.write( "So a = 4\r<BR>\n" );
document.write( "\n" );
document.write( "Since four numbers in GP are...a/r, a, ar, ar^2<BR>\n" );
document.write( "Therefore four numbers in GP are...<BR>\n" );
document.write( "4/4, 4, 4*4, 4*4^2<BR>\n" );
document.write( "1, 4, 16, 64\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );