document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66123>Question 66123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for all real roots\r<BR>\n" );
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document.write( "(sqrt)z-(sqrt)(z-1)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46860 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need to solve for all real roots\r<BR>\n" );
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document.write( "(sqrt)z-(sqrt)(z-1)=1\r<BR>\n" );
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document.write( "First, we'll square both sides to start getting rid of the radicals:\r<BR>\n" );
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document.write( "[sqrt(z)-sqrt(z-1)]^2=(sqrt(z))^2-2(sqrt(z))(sqrt(z-1))+(sqrt(z-1))^2\r<BR>\n" );
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document.write( "so we have:\r<BR>\n" );
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document.write( "z-2sqrt((z)(z-1))+z-1=1 which equals\r<BR>\n" );
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document.write( "2z-1-2sqrt((z)(z-1))=1  Now, we'll subtract 2z and -1 from both sides:\r<BR>\n" );
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document.write( "-2sqrt((z)(z-1))=1-2z+1=\r<BR>\n" );
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document.write( "-2sqrt((z)(z-1))=2-2z  divide both sides by -2\r<BR>\n" );
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document.write( "sqrt((z)(z-1))=z-1  square both sides again:\r<BR>\n" );
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document.write( "(z)(z-1)=(z-1)(z-1)  \r<BR>\n" );
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document.write( "Note:  We are to this point and the tendency is to divide both sides by (z-1) and that would be a BIG mistake.  Why??????????????\r<BR>\n" );
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document.write( "(z)(z-1)=(z-1)(z-1)=<BR>\n" );
document.write( "z^2-z=z^2-2z+1 subtract z^2 and -2z from both sides:\r<BR>\n" );
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document.write( "z^2-z^2-z+2z=1\r<BR>\n" );
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document.write( "z=1 is the only real solution:\r<BR>\n" );
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document.write( "AN IMPORTANT LESSON HERE:\r<BR>\n" );
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document.write( "z-1=0  AND YOU CAN'T DIVIDE BY 0\r<BR>\n" );
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document.write( "Hope this helps-----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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