document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249047>Question 249047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Two consecutive integers are added. The square of their sum is 361. What are the integers ?\r<BR>\n" );
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document.write( "2) The product of two consecutive even numbers is 288. What are the numbers ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181458 by </B><A HREF=/tutors/aboutme.mpl?userid=actuary><B>actuary(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=actuary><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=181458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PROBLEM 1\r<BR>\n" );
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document.write( "Let n = the first integer, so n+1 is the next integer.  Now translate the word problem into an algebraic expresion.  So, (n+(n+1))^2=361.  Take the square root of both sides of the equation, so, n+(n+1)=19 and n+(n+1)=-19.\r<BR>\n" );
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document.write( "Case 1 yields the following linear equation 2n+1=19.  Solving this linear equation results in the value n = (19-1)/2=9. The pair is 9 and 10 \r<BR>\n" );
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document.write( "Case 2 yields the folowing linear equation n+(n+1)=-19.  Solving this linear equation results in the value for n = (-19-1)/2=-10.  The pair is then -10 <BR>\n" );
document.write( "and -9.\r<BR>\n" );
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document.write( "Problem 2 \r<BR>\n" );
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document.write( "Let n = the first even integer.  So n = 2k for some k. The next even integer is then n+2 = 2k+2.  Therefore, the words of the problem can be translated into the following algebraic equation  2k*(2k+2)=288.  Expanding this equation we have 4k^2+4k-288=0.  Dividing both sides by 4 produces k^2+k-72=0.  This equation can be solved for k by factoring. k^2+k-72=(k+9)(k-8)=0.  Therefore, <BR>\n" );
document.write( "k=-9 and k=8.  So,  the first pair of integers is n=2*k = -18 and the second integer is -16.\r<BR>\n" );
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document.write( "The second pair of integers is 2*8=16 and 18.\r<BR>\n" );
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document.write( "It is important to recognize the pairs of solutions for each question.\r<BR>\n" );
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document.write( "Good luck with your study of math.\r<BR>\n" );
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document.write( "Larry </SPAN>\n" );
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