document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398436>Question 398436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3 children are pythagorean triple at ages 6, 8, and 10. Will they be pythagorean triples again?  Show the formula that gave you that answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282373 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=282373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to find if there is some Pythagorean triple {x, x+2, x+4}, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+6 ALIGN=MIDDLE  ALT=\"x+%3C%3E+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since x+4 is the longest side,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%2B2%29%5E2+=+%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B2%29%5E2+=+%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%5E2+%2B+4x+%2B+4%29+=+x%5E2+%2B+8x+%2B+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%5E2+%2B+4x+%2B+4%29+=+x%5E2+%2B+8x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Moving everything to one side,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+-+12+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29%28x+%2B+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+6%29%28x+%2B+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> x = 6 or x = -2. However, x cannot be negative, so the only triple is when x = 6, and they will never be Pythagorean triples again. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );