document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035971>Question 1035971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a, b, c, d are in continued proportion, prove that a^3 + b^3 + c^3 : b^3 + c^3 + d^3 = a : d. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650630 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=650630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a, b, c, d in continued proportion ==> a/b = b/c = c/d = k for some constant of proportionality k \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+bk+=+ck%5E2+=+dk%5E3 ALIGN=MIDDLE  ALT=\"a+=+bk+=+ck%5E2+=+dk%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+a%281%2Fk%29 ALIGN=MIDDLE  ALT=\"b+=+a%281%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+a%281%2Fk%29%5E2 ALIGN=MIDDLE  ALT=\"c+=+a%281%2Fk%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+a%281%2Fk%29%5E3 ALIGN=MIDDLE  ALT=\"d+=+a%281%2Fk%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so a,b,c, and d form a geometric sequence.\r<BR>\n" );
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document.write( "==><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%2Bb%5E3%2Bc%5E3%29%2F%28b%5E3%2Bc%5E3%2Bd%5E3%29+=+%28a%5E3%2Ba%5E3%2A%281%2Fk%5E3%29%2Ba%5E3%2A%281%2Fk%5E6%29%29%2F%28a%5E3%2A%281%2Fk%5E3%29%2Ba%5E3%2A%281%2Fk%5E6%29%2Ba%5E3%2A%281%2Fk%5E9%29%29+=+%281%2B1%2Fk%5E3%2B1%2Fk%5E6%29%2F%281%2Fk%5E3%2B1%2Fk%5E6%2B1%2Fk%5E9%29+=1%2F%28+1%2Fk%5E3%29+=+k%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "BUT, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+dk%5E3 ALIGN=MIDDLE  ALT=\"a+=+dk%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E3+=+a%2Fd ALIGN=MIDDLE  ALT=\"k%5E3+=+a%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the statement is proved. </SPAN>\n" );
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