document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129112>Question 129112</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1885145691/algebrahomeworkh>ALGEBRA 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Here is the problem in exact words. <BR>\n" );
document.write( "3,4,5 and 7,24,25 are examples of a Pythagorean Triple. Pythagorean Triples are made up of whole numbers. These two examples are special because in both cases the hypotenuse is 1 greater than the longer leg.\r<BR>\n" );
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document.write( "Find one where one of the legs is 37 and the hypotenuse is one more than th longer leg. \r<BR>\n" );
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document.write( "I really need help with this. Please try to get back to me as soon as possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94384 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two possibilities:\r<BR>\n" );
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document.write( "First, the longer leg could be 37, then the hypotenuse is 38, and the shorter leg is the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38%5E2-37%5E2 ALIGN=MIDDLE  ALT=\"38%5E2-37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38%5E2-37%5E2=1444-1369=75 ALIGN=MIDDLE  ALT=\"38%5E2-37%5E2=1444-1369=75\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since 75 is not a perfect square, this is not the correct answer.\r<BR>\n" );
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document.write( "The other possibility is that 37 is the short leg, x is the long leg, and x + 1 is then the hypotenuse.  Using Pythagoras:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B37%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=x%5E2%2B1369 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=x%5E2%2B1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=1369 ALIGN=MIDDLE  ALT=\"2x%2B1=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=1368 ALIGN=MIDDLE  ALT=\"2x=1368\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=684 ALIGN=MIDDLE  ALT=\"x=684\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the Pythagorean triple is 37, 684, 685.  I'll leave it as a exercise for you to do the arithmetic and prove it. </SPAN>\n" );
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