document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73945>Question 73945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Plz solve this...<BR>\n" );
document.write( "1) If the arithematic mean between two numbers is twice there geometric mean then prove that the ratio of 2 nos. is (2+sqrt3):(2-sqrt3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52962 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=52962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the arithmetic mean between two numbers is twice their geometric mean then prove that the ratio of 2 nos. is (2+sqrt3):(2-sqrt3)<BR>\n" );
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document.write( "Let a,b be the two numbers:<BR>\n" );
document.write( "arithmetic mean = (a+b)/2<BR>\n" );
document.write( "geometric mean = sqrt(ab)<BR>\n" );
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document.write( "EQUATIONS:\r<BR>\n" );
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document.write( "(a+b)/2 = 2(sqrt(ab))<BR>\n" );
document.write( "a+b = 4sqrt(ab)<BR>\n" );
document.write( "square both sides to get:<BR>\n" );
document.write( "(a+b)^2 = 16ab<BR>\n" );
document.write( "a^2-14ab+b^2=0<BR>\n" );
document.write( "Use the Quadratic formula to solve for \"a\" in terms of \"b\":<BR>\n" );
document.write( "a=[14b+-sqrt((14b)^2-4b^2)]/2\r<BR>\n" );
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document.write( "a=[14b+-sqrt(192b^2)]/2\r<BR>\n" );
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document.write( "a=[14b+-4b(sqrt3)]/2\r<BR>\n" );
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document.write( "a = [7 +- (2sqrt3)b]\r<BR>\n" );
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document.write( "a:b = (7+2sqrt(3)):1<BR>\n" );
document.write( "or a:b =(7-2sqrt(3)):1\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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