document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208349>Question 1208349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle.\r<BR>\n" );
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document.write( "Here is my set up:\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2\r<BR>\n" );
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document.write( "(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846715 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle.\r<BR>\n" );
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document.write( "Here is my set up:\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2\r<BR>\n" );
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document.write( "(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is posed INCORRECTLY.\r<BR>\n" );
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document.write( "Indeed, if m and n are opposite integers and m > n, it means that m is a positive integer number, <BR>\n" );
document.write( "while n is a negative integer number, n = -m.\r<BR>\n" );
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document.write( "Then  b = 2mn is a negative number.\r<BR>\n" );
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document.write( "But negative number can not express the length of the side of a triangle.<BR>\n" );
document.write( "</pre>\r<BR>\n" );
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document.write( "This my reasoning proves that the problem formulation in the post is TOTALLY, GLOBALLY and FATALLY defective.\r<BR>\n" );
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document.write( "I don't know, from which source did you get this gibberish.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If to remove the word \"opposite\" from the condition and replace it by \"positive\", <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then the problem would be correct and your setup/idea  a^2 + b^2 = c^2 would be correct.\r<BR>\n" );
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document.write( "But your next equation, \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2\r<BR>\n" );
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document.write( "is written incorrectly.\r<BR>\n" );
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document.write( "Its correct version is\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2.\r<BR>\n" );
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document.write( "//////////////////////\r<BR>\n" );
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document.write( "<U>Comment from student</U>: I made a typo. The correct problem is this one: Suppose that m and n are positive integers with m > n. <BR>\n" );
document.write( "If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides <BR>\n" );
document.write( "of a right triangle. My set up is now correct. True?\r<BR>\n" );
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document.write( "<U>My response</U>:  I just explained to you, where is your next error.\r<BR>\n" );
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document.write( "Your next equation, \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2\r<BR>\n" );
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document.write( "is written incorrectly.\r<BR>\n" );
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document.write( "Its correct version is\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2.\r<BR>\n" );
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document.write( "..........................................\r<BR>\n" );
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document.write( "You see, it's very difficult to discuss your work, since you make mistakes in every line.\r<BR>\n" );
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document.write( "You should make your work more responsibly.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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