document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127615>Question 127615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a scientet makes two measurements x1 and x2 of a quantity whose true measure x is not known. The errors are then x-x1 and x-x2. What number can be assigned to x so that the sum of the squares is a mininum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93513 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=93513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose a scientet makes two measurements x1 and x2 of a quantity whose true measure x is not known. The errors are then x-x1 and x-x2. What number can be assigned to x so that the sum of the squares is a mininum?<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "SS = (x-x1)^2 + (x-x2)^2<BR>\n" );
document.write( "SS = (x^2-2x1x+x1^2 + x^2-2x2x+x^2^2<BR>\n" );
document.write( "SS = 2x^2 -2(x1+x2)x + x1^2+x2^2<BR>\n" );
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document.write( "The minimum occurs at x = -b/2a <BR>\n" );
document.write( "= (2(x1+x2)/4)<BR>\n" );
document.write( "= (x1+x^2)/2<BR>\n" );
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document.write( "You will get a minimum when x = (x1+x2)/2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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