document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704504>Question 704504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this false proof and what is the mistake in the proof?<BR>\n" );
document.write( "a=1,b=1<BR>\n" );
document.write( "a=b<BR>\n" );
document.write( "a2=ab<BR>\n" );
document.write( "a2+a2=a2+ab<BR>\n" );
document.write( "2a2=a2+ab<BR>\n" );
document.write( "2a2-2ab=a2-ab<BR>\n" );
document.write( "2(a2-ab)= 1(a2-ab)<BR>\n" );
document.write( "2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434116 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=434116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You let/force a = b. \r<BR>\n" );
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document.write( "So because a = b, this means that \r<BR>\n" );
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document.write( "a^2 - ab\r<BR>\n" );
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document.write( "b^2 - b*b ... plug in a = b (ie replace all copies of 'a' with 'b')\r<BR>\n" );
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document.write( "b^2 - b^2\r<BR>\n" );
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document.write( "0\r<BR>\n" );
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document.write( "So if a = b, then a^2 - ab is equal to 0. \r<BR>\n" );
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document.write( "When you jump from 2(a^2-ab)= 1(a^2-ab) to 2 = 1 in the last two lines, you are dividing both sides by a^2-ab. But if a = b, then a^2-ab = 0, which means you're dividing both sides by zero...which is undefined.\r<BR>\n" );
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document.write( "So the last step is NOT a valid algebraic move because you can't divide by zero.\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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