document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703375>Question 703375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive positive integers is seventeen seventy-two. Write an equation that can be used to find the two integers. What are the integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433483 by </B><A HREF=/tutors/aboutme.mpl?userid=nshah11><B>nshah11(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nshah11><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=433483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that since the integers are positive and consecutive, let them be represented by x and (x + 1). \r<BR>\n" );
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document.write( "Reciprocal of x => 1/x\r<BR>\n" );
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document.write( "Reciprocal of (x + 1) => 1/(x + 1)\r<BR>\n" );
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document.write( "1/x + 1/(x + 1) = 1772\r<BR>\n" );
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document.write( "Getting a common denominator of x(x + 1):\r<BR>\n" );
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document.write( "(x + 1) + x = 1772(x)(x + 1)\r<BR>\n" );
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document.write( "2x + 1 = 1772x^2 + 1772x\r<BR>\n" );
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document.write( "1772x^2 + 1770x - 1 = 0\r<BR>\n" );
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document.write( "Via the quadratic formula:\r<BR>\n" );
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document.write( "x = (-1770 +/- &#8730;(1770^2 - 4(1772)(-1))/(2*1772) yields no integers at all. Pleas recheck your problem. </SPAN>\n" );
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