document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182365>Question 182365</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321506429/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The product of two consecutive integers is 4 less than four times their sum. Find 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 #136987 by </B><A HREF=/tutors/aboutme.mpl?userid=mastermath><B>mastermath(14)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mastermath><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=136987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the consecutive numbers be n and (n+1) respectively.<BR>\n" );
document.write( "Their sum is (n + n + 1) = (2n + 1)<BR>\n" );
document.write( "Four times their sum = 4(2n + 1)<BR>\n" );
document.write( "The product of the numbers = n(n + 1)<BR>\n" );
document.write( "The product of two consecutive integers is 4 less than four times their sum.<BR>\n" );
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document.write( "So, the equation becomes<BR>\n" );
document.write( "n(n + 1) = 4 (2n + 1) - 4<BR>\n" );
document.write( "n^2 + n = 8n + 4 - 4<BR>\n" );
document.write( "n^2 + n = 8n<BR>\n" );
document.write( "Subtract 8n on both the sides<BR>\n" );
document.write( "n^2 + n - 8n = 8n - 8n<BR>\n" );
document.write( "n^2 - 7n = 0<BR>\n" );
document.write( "n (n - 7) = 0<BR>\n" );
document.write( "Use the zero product rule<BR>\n" );
document.write( "n=0 or (n-7)=0<BR>\n" );
document.write( "n=0 or n=7.<BR>\n" );
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document.write( "If n=0, n+1 = 0 + 1 = 1.<BR>\n" );
document.write( "So, one pair of consecutive integers is 0 and 1.<BR>\n" );
document.write( "If n=7, n+1 = 7 + 1 = 8.<BR>\n" );
document.write( "So, second pair of consecutive integers is 7 and 8. <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Mastermath.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );