document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252191>Question 252191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit number has different digits. If the difference between the square of the number and the square of the number whose digits are interchanged is a positive perfect square, what is the two digit number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183961 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=183961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let 10T + U be the first digit, where T can't = U.<BR>\n" );
document.write( "Let 10U + T be the second, reversed digits, number, where T can't = U.<BR>\n" );
document.write( "From the question, we then get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810T%2BU%29%5E2+-+%2810U%2BT%29%5E2+=+X%5E2 ALIGN=MIDDLE  ALT=\"%2810T%2BU%29%5E2+-+%2810U%2BT%29%5E2+=+X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100T%5E2+%2B+20UT+%2B+U%5E2+-100U%5E2+-+20UT+-+T%5E2+=+x%5E2 ALIGN=MIDDLE  ALT=\"100T%5E2+%2B+20UT+%2B+U%5E2+-100U%5E2+-+20UT+-+T%5E2+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we can see that the UT parts cancel. After combining like terms, this leaves us with\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99T%5E2+-+99U%5E2+=+X%5E2 ALIGN=MIDDLE  ALT=\"99T%5E2+-+99U%5E2+=+X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99%28T%5E2-U%5E2%29 ALIGN=MIDDLE  ALT=\"99%28T%5E2-U%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = X^2}}}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%28%2811%29%2A%28T%2BU%29%28T-U%29%29+=+X%5E2 ALIGN=MIDDLE  ALT=\"3%2Asqrt%28%2811%29%2A%28T%2BU%29%28T-U%29%29+=+X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "SInce 6+5 = 11 and 6-5 = 1, T = 6 and U = 5, we get\r<BR>\n" );
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document.write( "65^2 - 56^2 = 4225 - 3136 = 1089 = 33^2. </SPAN>\n" );
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