document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733314>Question 733314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find two consecutive positive integers such that the sum of their squares is 61 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448354 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=448354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let i represent a positive integer and i+1 be the consecutive integer.  We know that<BR>\n" );
document.write( "       i squared + (i+1)squared = 61\r<BR>\n" );
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document.write( "squaring both terms\r<BR>\n" );
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document.write( "        i squared + i squared + 2i + 1 = 61\r<BR>\n" );
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document.write( "combining terms  and subtracting 1 from both sides of equal sign we have\r<BR>\n" );
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document.write( "        2 i squared + 2i = 60\r<BR>\n" );
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document.write( "divide equation by 2\r<BR>\n" );
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document.write( "         i squared + i = 30\r<BR>\n" );
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document.write( "we now have the quadratic equation\r<BR>\n" );
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document.write( "         i squared + i - 30 = 0\r<BR>\n" );
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document.write( "factoring the quadratic equation, we have\r<BR>\n" );
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document.write( "        ( i + 6 ) * (i - 5) = 0\r<BR>\n" );
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document.write( "this gives us two equations\r<BR>\n" );
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document.write( "      i + 6 = 0 and i - 5 = 0\r<BR>\n" );
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document.write( "now the integers are required to be positive so the solution is\r<BR>\n" );
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document.write( "      i = 5 and i+1 = 6\r<BR>\n" );
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document.write( "and we see that\r<BR>\n" );
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document.write( "       5 squared + 6 squared = 61\r<BR>\n" );
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document.write( "namely,\r<BR>\n" );
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document.write( "         25 + 36 = 61\r<BR>\n" );
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document.write( "         </SPAN>\n" );
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