document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992486>Question 992486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide 16 into two parts such that the square of the bigger number is 64 more than the square of the smaller number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612099 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We divide 16 into two parts/numbers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=16 ALIGN=MIDDLE  ALT=\"x%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and we say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the bigger number, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the smaller number.<BR>\n" );
document.write( "It is not explicitly stated, but I suspect that the wording implies that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > are both positive numbers, and probably positive integers.<BR>\n" );
document.write( "The phrase \"the square of the bigger number is 64 more than the square of the smaller number\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=y%5E2%2B64 ALIGN=MIDDLE  ALT=\"x%5E2=y%5E2%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2=64 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now we have a system of two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2-y%5E2=64%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2-y%5E2=64%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2=y%5E2%2B64%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2=y%5E2%2B64%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "From there, we can take different roads to the solution.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "ONE WAY:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2-y%5E2=64%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2-y%5E2=64%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%28x%2By%29%28x-y%29=64%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28%28x%2By%29%28x-y%29=64%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%28x%2By%29%28x-y%29%2F%28x%2By%29=64%2F16%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28%28x%2By%29%28x-y%29%2F%28x%2By%29=64%2F16%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-y=4%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x-y=4%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-y%2Bx%2By=4%2B16%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x-y%2Bx%2By=4%2B16%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x=20%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%282x=20%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2C10%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2C10%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2Cy=16-10%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2Cy=16-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=10%2Cy=6%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=10%2Cy=6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ANOTHER WAY:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2=y%5E2%2B64%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2=y%5E2%2B64%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2=%2816-x%29%5E2%2B64%2Cy=16-x%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2=%2816-x%29%5E2%2B64%2Cy=16-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2=256-32x%2Bx%5E2%2B64%2Cy=16-x%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2=256-32x%2Bx%5E2%2B64%2Cy=16-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%280=320-32x%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%280=320-32x%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2832x=320%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%2832x=320%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=320%2F32%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x=320%2F32%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2Cx%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2Cx%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2C10%2By=16%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2C10%2By=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10%2Cy=16-10%29 ALIGN=MIDDLE  ALT=\"system%28x=10%2Cy=16-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=10%2Cy=6%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=10%2Cy=6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "A \"CHEATING\" WAY:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=y%5E2%2B64 ALIGN=MIDDLE  ALT=\"x%5E2=y%5E2%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=y%5E2%2B8%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=y%5E2%2B8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A right triangle with legs measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a hypotenuse measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Look up a table of Pythagorean triples.<BR>\n" );
document.write( "In that table you would find, in the first two columns,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (not necessarily in that order.<BR>\n" );
document.write( "The third column will show <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In the first few rows you find two choices:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C3%2C6%2C8%2C10%2C8%2C15%2C17%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C3%2C6%2C8%2C10%2C8%2C15%2C17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first choice gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6%2Cx=10%2Cx%2B10=6%2B10=16%29 ALIGN=MIDDLE  ALT=\"y=6%2Cx=10%2Cx%2B10=6%2B10=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and shows you the solution.<BR>\n" );
document.write( "The other row shows<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15%2Cx=17%2Cx%2By=15%2B17=32%29 ALIGN=MIDDLE  ALT=\"y=15%2Cx=17%2Cx%2By=15%2B17=32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and has nothing to do with the solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );