document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6273>Question 6273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers with a geometric mean of sqrt 24 given that one number is two more than the other. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3370 by </B><A HREF=/tutors/aboutme.mpl?userid=xcentaur><B>xcentaur(357)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=xcentaur><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the numbers be a and b.<BR>\n" );
document.write( "then geometric mean=(a+b)/2<BR>\n" );
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document.write( "given second number is two greater that first,b=a+2<BR>\n" );
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document.write( "therefore geometric mean=(a+a+2)/2=(2a+2)/2=[2(a+1)]/2=(a+1)<BR>\n" );
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document.write( "From the question,it is required geometric mean be equal to sqrt24.<BR>\n" );
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document.write( "Then we get,<BR>\n" );
document.write( "a+1=sqrt(24)<BR>\n" );
document.write( "(a+1)=sqrt(2*2*2*3)<BR>\n" );
document.write( "(a+1)=2sqrt(6)<BR>\n" );
document.write( "a=2sqrt(6)-1<BR>\n" );
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document.write( "then value of b=a+2<BR>\n" );
document.write( "=2sqrt(6)-1+2<BR>\n" );
document.write( "=2sqrt(6)+1<BR>\n" );
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document.write( "cross check:<BR>\n" );
document.write( "geometric mean of [2sqrt(6)-1] and [2sqrt(6)+1] is=<BR>\n" );
document.write( "={[2sqrt(6)-1]+[2sqrt(6)+1]}/2<BR>\n" );
document.write( "={2[2sqrt(6)]}/2<BR>\n" );
document.write( "=2sqrt(6)<BR>\n" );
document.write( "which is equal to sqrt(24)<BR>\n" );
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document.write( "Hence these numbers are correct<BR>\n" );
document.write( "<b>[2sqrt(6)-1]<br><BR>\n" );
document.write( "[2sqrt(6)+1]</b><BR>\n" );
document.write( "<br>Hope this helps,<BR>\n" );
document.write( "good luck. </SPAN>\n" );
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