document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066287>Question 1066287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find 3 number in the geometrical progression whose sum is 28 and whose product is 512 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681454 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a be the first number, b be the 2nd, c be the 3rd.\r<BR>\n" );
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document.write( "So a + b + c = 28 and  a*b*c = 512.\r<BR>\n" );
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document.write( "Normally this would not be enough, but we know that there is a progression.\r<BR>\n" );
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document.write( "Let  r be the common ratio between numbers in a geometric progression.\r<BR>\n" );
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document.write( "So the 2nd number can be written as:<BR>\n" );
document.write( "b = r*a\r<BR>\n" );
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document.write( "And the 3rd number can be written as:\r<BR>\n" );
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document.write( "c = r^2*a\r<BR>\n" );
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document.write( "Go back to our original problem.\r<BR>\n" );
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document.write( "a + b + c  can be written as  a + ra + r^2*a\r<BR>\n" );
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document.write( "a*b*c  can be written as  a * (ra) * (r^2*a) =  r^3*a^3\r<BR>\n" );
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document.write( "so we have that two equations.\r<BR>\n" );
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document.write( "a+ra+r^2*a = 28<BR>\n" );
document.write( "r^3*a^3 = 512\r<BR>\n" );
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document.write( "We can solve for ra  by taking the cube root of both sides in the 2nd equation.\r<BR>\n" );
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document.write( "(r*a)^3  = 512\r<BR>\n" );
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document.write( "(r*a) = 8\r<BR>\n" );
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document.write( "So a = 8/r\r<BR>\n" );
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document.write( "8/r +  8 + 8r = 28\r<BR>\n" );
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document.write( "8/r + 8r = 20\r<BR>\n" );
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document.write( "8(1/r + r) = 20\r<BR>\n" );
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document.write( "(r^2+1 / r) = 5/2\r<BR>\n" );
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document.write( "2(r^2+ 1) = 5r\r<BR>\n" );
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document.write( "2r^2 + 2 = 5r\r<BR>\n" );
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document.write( "2r^2 - 5r +2 = 0\r<BR>\n" );
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document.write( "we can rewrite as  (2r-1)(r-2) so  r = 1/2 or r = 2.\r<BR>\n" );
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document.write( "Let's try r = 2 first.\r<BR>\n" );
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document.write( "So  if  r =2 then a = 4\r<BR>\n" );
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document.write( "So we have \r<BR>\n" );
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document.write( "4, 8, 16 which do satisfy the conditions. But are there other numbers?\r<BR>\n" );
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document.write( "Try  r = 1/2.   Then  a = 16.\r<BR>\n" );
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document.write( "So we have 16, 8 , 4. Ah, so it appears it is the same either way.\r<BR>\n" );
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document.write( "The numbers are 4, 8 , 16.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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