document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859547>Question 859547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It would be greatly appreciated if you would be able to help me with:<BR>\n" );
document.write( "    Find three consecutive, positive integers such that the square of the smallest exceeds the largest by 10.\r<BR>\n" );
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document.write( "I've attempted to solve this by doing:<BR>\n" );
document.write( "(x+1)(x+2)(x+3)=10<BR>\n" );
document.write( "As I'm not very familiar with verbal algebraic terms, I have trouble breaking down world problems.\r<BR>\n" );
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document.write( "Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517816 by </B><A HREF=/tutors/aboutme.mpl?userid=Awesom3guy><B>Awesom3guy(31)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Awesom3guy><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=517816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "You are looking for three consecutive numbers:<BR>\n" );
document.write( "x, x+1, and x+2.<BR>\n" );
document.write( "There's no need to make it x+1 on the first one.\r<BR>\n" );
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document.write( "The square of the smallest number exceeds the largest number by 10.<BR>\n" );
document.write( "So the square of the smallest number is larger than the biggest number by 10.<BR>\n" );
document.write( "Now you just need to put that in math language. It's REALLY not hard.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%28x%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"x%5E2+=+%28x%2B2%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You have a quadratic equation which you need to simplify and put in standard form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+x+%2B+12 ALIGN=MIDDLE  ALT=\"x%5E2+=+x+%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+-+x+-+12+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+x+-+12+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you solve for x - break the middle term into two parts so that you can factor the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-4x+%2B+3x+-+12+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-4x+%2B+3x+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%28x+-+4%29+%2B+3%2A%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"x%2A%28x+-+4%29+%2B+3%2A%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%2A%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%2A%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Two options:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which gives x = -3. This obviously isn't the solution as we are looking for two consecutive POSITIVE integers.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which gives x = 4.\r<BR>\n" );
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document.write( "Now that you have the first number, you know that the other two are 5 and 6.<BR>\n" );
document.write( "So the three integers are 4, 5 and 6.\r<BR>\n" );
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document.write( "Also check - does the square of 4 exceed 6 by 10?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+-+6+=+16+-+6+=+10 ALIGN=MIDDLE  ALT=\"4%5E2+-+6+=+16+-+6+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All good :) </SPAN>\n" );
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