document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=594645>Question 594645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When verifying an identity, why can't you square both sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376854 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=376854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Squaring both sides essentially weakens a statement. For example, suppose that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = 1\">\r<BR>\n" );
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document.write( "Squaring both sides yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2 = 1\">\r<BR>\n" );
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document.write( "However the second equation is not equivalent to the first one, as x could equal 1 or -1. You can square both sides when dealing with \"if and only if\" relations, for example, if you know that x must be positive. </SPAN>\n" );
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