document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56029>Question 56029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am solving the following equation:\r<BR>\n" );
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document.write( "sqrt x-1 = x-3\r<BR>\n" );
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document.write( "I get 5 but then I did it again and got 2.  HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37993 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=37993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt (x-1) = x-3 <BR>\n" );
document.write( "square both sides to get:<BR>\n" );
document.write( "x-1= x^2-6x+9<BR>\n" );
document.write( "x^2-7x+10=0<BR>\n" );
document.write( "(x-5)(x-2)=0<BR>\n" );
document.write( "x=5 or x=2<BR>\n" );
document.write( "Checking these answers:<BR>\n" );
document.write( "Checking x=5 you get:<BR>\n" );
document.write( "sqrt(5-1)=5-3<BR>\n" );
document.write( "2=2<BR>\n" );
document.write( "x=5 is a good solution<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Checking s=2 you get:<BR>\n" );
document.write( "sqrt(2-1)=2-3<BR>\n" );
document.write( "sqrt 1 =-1<BR>\n" );
document.write( "1 = -1<BR>\n" );
document.write( "That is wrong so x=2 is an extraneous solution which <BR>\n" );
document.write( "means it is a solution for the algebra that resulted<BR>\n" );
document.write( "while solving the problem but it is not a solution of<BR>\n" );
document.write( "the original problem.<BR>\n" );
document.write( "Where did it come from?  It resulted from squaring the<BR>\n" );
document.write( "original problem; that introduced a solution that worked<BR>\n" );
document.write( "for the squared expression but not for the original <BR>\n" );
document.write( "expression.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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