document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=635117>Question 635117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help.  I do not understand any of this.\r<BR>\n" );
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document.write( "I need to build or generate at least five more Pythagorean Triples using one of the many formulas available. After building your triples, verify each of them in the Pythagorean Theorem equation. The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.\r<BR>\n" );
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document.write( "Thank you for any help you can give me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #400165 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=400165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> generate at least five more Pythagorean Triples using one of the many formulas available. <BR>\n" );
document.write( "After building your triples, verify each of them in the Pythagorean Theorem equation.<BR>\n" );
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document.write( "Euclid's formula for generating triples, given an arbitrary pair of positive<BR>\n" );
document.write( "integers, m and n, where m > n. a^2 + b^2 = c^2<BR>\n" );
document.write( "a = m^2 - n^2<BR>\n" );
document.write( "b = 2mn<BR>\n" );
document.write( "c = m^2 + n^2<BR>\n" );
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document.write( "Choose numbers less than 10<BR>\n" );
document.write( "Example1; m=3, n=2<BR>\n" );
document.write( "a = 3^2 - 2^2 = 9 - 4 = 5<BR>\n" );
document.write( "b = 2(3*2) = 12<BR>\n" );
document.write( "c = 3^2 + 2^2 = 13<BR>\n" );
document.write( "So we have a triple: 5, 12, 13<BR>\n" );
document.write( "5^2 + 12^2 = 13^2<BR>\n" );
document.write( "25 + 144 = 169<BR>\n" );
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document.write( "Example 2: m=7, n=3<BR>\n" );
document.write( "a = 49-9 = 40<BR>\n" );
document.write( "b = 2(7*3) = 42<BR>\n" );
document.write( "c = 49 + 9 = 58 <BR>\n" );
document.write( "a=40, b=42, c=58<BR>\n" );
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document.write( "Example 3: m=9, m=5<BR>\n" );
document.write( "a = 81 - 25 = 56<BR>\n" );
document.write( "b = 2(9*5) = 90<BR>\n" );
document.write( "c = 81 + 25 = 106<BR>\n" );
document.write( "a=56, b=90, c = 106<BR>\n" );
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document.write( "You should be able to generate a few more using this method, <BR>\n" );
document.write( "check them on your calc enter: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find c </SPAN>\n" );
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