document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243740>Question 243740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to figure out this problem:\r<BR>\n" );
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document.write( "THis is how the word problem is written in the book:\r<BR>\n" );
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document.write( "Find three consecutive even intergers such that the square of the largest exceeds the sum of the squares of the other two by 12. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178554 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=178554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For most problems like this, your best interest is served by using as few variables as possible.  For example, the setup says \"3 consecutive EVEN integers,\" which is a temptation to call x, y, and z.<BR>\n" );
document.write( "But from what we know about consecutive numbers, they're just 1 apart.  Consecutive EVEN integers are 2 apart.  So we can define the 3 unknown numbers in terms of x.<BR>\n" );
document.write( "a = x<BR>\n" );
document.write( "b = x+2<BR>\n" );
document.write( "c = x+4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We're all told the square of the largest number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 12 more than the sum of the squares of the other two numbers.  We can write this fact as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%2B2%29%5E2+%2B+12 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B2%29%5E2+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Combining we have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2+=+x%5E2+%2B+%28x%2B2%29%5E2+%2B+12 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2+=+x%5E2+%2B+%28x%2B2%29%5E2+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Resolving the squares.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%2B4%29+=+x%5E2+%2B+%28x%2B2%29%28x%2B2%29+%2B+12 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%2B4%29+=+x%5E2+%2B+%28x%2B2%29%28x%2B2%29+%2B+12\"   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+%2B+4x+%2B+4x+%2B+16+=+x%5E2+%2B+x%5E2+%2B+2x+%2B+2x+%2B+4+%2B+12 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+%2B+4x+%2B+16+=+x%5E2+%2B+x%5E2+%2B+2x+%2B+2x+%2B+4+%2B+12\"   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+%2B+8x+%2B+16+=+2x%5E2+%2B+4x+%2B+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8x+%2B+16+=+2x%5E2+%2B+4x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Collecting like terms<BR>\n" );
document.write( "Subtract x^2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+%2B+16+=+x%5E2+%2B+4x+%2B+16 ALIGN=MIDDLE  ALT=\"8x+%2B+16+=+x%5E2+%2B+4x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 8x from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+x%5E2+-+4x+=+16 ALIGN=MIDDLE  ALT=\"16+=+x%5E2+-+4x+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 16 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+4x ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+4x\"   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+-+4x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can factor an 'x' from the left-hand.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-4%29=0 ALIGN=MIDDLE  ALT=\"x%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we have two possible solutions:<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "x=4<BR>\n" );
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document.write( "Testing x=0.<BR>\n" );
document.write( "0^2 = 0<BR>\n" );
document.write( "2^2 = 4<BR>\n" );
document.write( "4^2 = 16<BR>\n" );
document.write( "Is 4^2 equal to the sum of the other two squares + 12?<BR>\n" );
document.write( "Yes.<BR>\n" );
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document.write( "Testing x=4.<BR>\n" );
document.write( "4^2 = 16<BR>\n" );
document.write( "6^2 = 36<BR>\n" );
document.write( "8^2 = 64<BR>\n" );
document.write( "Is 8^2 equal to the sum of the other two squares + 12?<BR>\n" );
document.write( "16+36=52, with is 12 less than 64.<BR>\n" );
document.write( "So this works, too.<BR>\n" );
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document.write( "The EVEN consecutive digits are:<BR>\n" );
document.write( "0, 2 & 4<BR>\n" );
document.write( "and<BR>\n" );
document.write( "4, 6 & 8<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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