document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87338>Question 87338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help. I need to find three consectutive integers such that the sum of their squares is 77. Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63259 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=63259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=1st #, y=2nd #, z=3rd #\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2Bz%5E2=77 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2Bz%5E2=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the translation of \"the sum of their (each number) squares is 77\"\r<BR>\n" );
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document.write( "Since each number is consecutive, we're really adding 1 each time. So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x%2B1%29%2B1=x%2B2 ALIGN=MIDDLE  ALT=\"z=%28x%2B1%29%2B1=x%2B2\"   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=x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=77 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2B2 ALIGN=MIDDLE  ALT=\"z=x%2B2\"   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=x%5E2%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B4x%2B4%29=77 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B4x%2B4%29=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x%2B5=77 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x%2B5=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x%2B5-77=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x%2B5-77=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 77 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x-72=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x-72=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now lets use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general form of the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B6%2Ax-72=0 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B6%2Ax-72=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=x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A3%2A-72+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A3%2A-72+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=6, and c=-72\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+36-4%2A3%2A-72+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36-4%2A3%2A-72+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 6 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+36%2B864+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36%2B864+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-72%2A3 ALIGN=MIDDLE  ALT=\"-4%2A-72%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=864 ALIGN=MIDDLE  ALT=\"864\"   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=x+=+%28-6+%2B-+sqrt%28+900+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+900+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+30%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+30%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+30%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+30%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B+30%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B+30%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+-+30%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+-+30%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24%2F6 ALIGN=MIDDLE  ALT=\"x=24%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-36%2F6 ALIGN=MIDDLE  ALT=\"x=-36%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B6%2Ax-72 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B6%2Ax-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-16%2C+14%2C+-16%2C+14%2C3%2Ax%5E2%2B6%2Ax%2B-72%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-16%2C+14%2C+-16%2C+14%2C3%2Ax%5E2%2B6%2Ax%2B-72%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This verifies our answer\r<BR>\n" );
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document.write( "So our first number could be 4 or -6\r<BR>\n" );
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document.write( "Lets use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the 2nd and 3rd number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2B1 ALIGN=MIDDLE  ALT=\"y=4%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=4%2B2 ALIGN=MIDDLE  ALT=\"z=4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=6 ALIGN=MIDDLE  ALT=\"z=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have 3 numbers: 4,5,6\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2%2B5%5E2%2B6%5E2=77 ALIGN=MIDDLE  ALT=\"4%5E2%2B5%5E2%2B6%5E2=77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2B25%2B36=77 ALIGN=MIDDLE  ALT=\"16%2B25%2B36=77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77=77 ALIGN=MIDDLE  ALT=\"77=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > works\r<BR>\n" );
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document.write( "So the 3 numbers 4,5,6 work\r<BR>\n" );
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document.write( "Now lets use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the 2nd and 3rd number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6%2B1 ALIGN=MIDDLE  ALT=\"y=-6%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-6%2B2 ALIGN=MIDDLE  ALT=\"z=-6%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-4 ALIGN=MIDDLE  ALT=\"z=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have 3 numbers: -6,-5,-4\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%5E2%2B%28-5%29%5E2%2B%28-4%29%5E2=77 ALIGN=MIDDLE  ALT=\"%28-6%29%5E2%2B%28-5%29%5E2%2B%28-4%29%5E2=77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2B25%2B16=77 ALIGN=MIDDLE  ALT=\"36%2B25%2B16=77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77=77 ALIGN=MIDDLE  ALT=\"77=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > works\r<BR>\n" );
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document.write( "So the 3 numbers -6,-5,-4 work\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So if you allow negative numbers, you get 2 possible answers\r<BR>\n" );
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document.write( "4,5,6\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "-6,-5,-4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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