document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107282>Question 107282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I cannot get anywhere with this problem, please help.\r<BR>\n" );
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document.write( "Find two consecutive positive integers such that the sum of their squares is 85. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78087 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "If consecutive integers starting at n, then their sum could be written as\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%2B+%28n%2B1%29+%2B+%28n%2B2%29+%2B...%2B+%28n%2Bk-1%29+ ALIGN=MIDDLE  ALT=\"n+%2B+%28n%2B1%29+%2B+%28n%2B2%29+%2B...%2B+%28n%2Bk-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since you have two consecutive integers, you weill use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%2B+%28n+%2B+1%29 ALIGN=MIDDLE  ALT=\"n+%2B+%28n+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to find two consecutive positive integers such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=the ALIGN=MIDDLE  ALT=\"the\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sum+ ALIGN=MIDDLE  ALT=\"+sum+\"   DISABLED_style= \"max-width:90%; height:auto;\" >of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=their+ ALIGN=MIDDLE  ALT=\"their+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=squares ALIGN=MIDDLE  ALT=\"squares\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85 ALIGN=MIDDLE  ALT=\"85\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you will have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+%28n+%2B+1%29%5E2+=+85 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+%28n+%2B+1%29%5E2+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+n%5E2+%2B+2n+%2B+1+=+85 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+n%5E2+%2B+2n+%2B+1+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2+%2B+2n+=+85+-+1 ALIGN=MIDDLE  ALT=\"2n%5E2+%2B+2n+=+85+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28n%5E2+%2B+n%29+=+84 ALIGN=MIDDLE  ALT=\"2%28n%5E2+%2B+n%29+=+84\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+n+=+42 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+n+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+n+-+42+=+0 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+n+-+42+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....writen in the standard form .....so you can apply quadratic formula to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and use only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+0 ALIGN=MIDDLE  ALT=\"n+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29 ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281%5E2+-4%2A1%2A%28-42%29+%29%29+%2F+%282%2A1%29 ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281%5E2+-4%2A1%2A%28-42%29+%29%29+%2F+%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281+%2B+168+%29%29+%2F+%282%29 ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281+%2B+168+%29%29+%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D=%28-1+%2B-+sqrt+%28169%29%29+%2F+%282%29 ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D=%28-1+%2B-+sqrt+%28169%29%29+%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%2C2%5D=%28-1+%2B-+13%29+%2F+%282%29 ALIGN=MIDDLE  ALT=\"n%5B1%2C2%5D=%28-1+%2B-+13%29+%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D=%28-1+%2B+13%29+%2F+%282%29 ALIGN=MIDDLE  ALT=\"n%5B1%5D=%28-1+%2B+13%29+%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....you will need just this one because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be positive number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D=%28+12%29+%2F+%282%29 ALIGN=MIDDLE  ALT=\"n%5B1%5D=%28+12%29+%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D=+6+ ALIGN=MIDDLE  ALT=\"n%5B1%5D=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >........this is first number\r<BR>\n" );
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document.write( "next consecutive number will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now check if the sum of their squares is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+85 ALIGN=MIDDLE  ALT=\"+85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+%2B+7%5E2+=+36+%2B+49+=+85 ALIGN=MIDDLE  ALT=\"6%5E2+%2B+7%5E2+=+36+%2B+49+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );