document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251986>Question 251986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"Word Problems Involving Products and Factoring\"\r<BR>\n" );
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document.write( "Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus 8 is the sum of their squares. can you solve this pls=(  tyty so much<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183720 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let:\r<BR>\n" );
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document.write( "x = first number<BR>\n" );
document.write( "x+1 = second number\r<BR>\n" );
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document.write( "product of (sum + diff) + 8 = sum (squares)\r<BR>\n" );
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document.write( "sum = x + x + 1 = 2x+1\r<BR>\n" );
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document.write( "diff = x + 1 - x = 1\r<BR>\n" );
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document.write( "product of sum and diff = (2x+1)*1 = 2x+1\r<BR>\n" );
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document.write( "sum of the squares is equal to the first number squared plus the second number squared.\r<BR>\n" );
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document.write( "deriving the sum of the squares, we get:\r<BR>\n" );
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document.write( "x^2 + (x+1)^2 equals:\r<BR>\n" );
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document.write( "x^2 + x^2 + 2x + 1\r<BR>\n" );
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document.write( "adding these together and combining like terms, we get:\r<BR>\n" );
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document.write( "x^2 + x^2 + 2x + 1 equals:\r<BR>\n" );
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document.write( "2x^2 + 2x + 1\r<BR>\n" );
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document.write( "since sum(squares) = product of sum and diff + 8, we get:\r<BR>\n" );
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document.write( "2x^2 + 2x + 1 = 2x + 1 + 8 which becomes:\r<BR>\n" );
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document.write( "2x^2 + 2x + 1 = 2x + 9\r<BR>\n" );
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document.write( "subtract 2x from both sides of the equation and subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2x^2 = 8\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
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document.write( "x^2 = 4\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get:\r<BR>\n" );
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document.write( "x = sqrt(4) = 2\r<BR>\n" );
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document.write( "answer should be x = 2\r<BR>\n" );
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document.write( "substitute in original problem statement equations to see if they are true.\r<BR>\n" );
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document.write( "sum of two numbers is 2 + 3 = 5\r<BR>\n" );
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document.write( "diff of two numbers is 3 - 2 = 1\r<BR>\n" );
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document.write( "product of sum and diff is 5*1 = 5\r<BR>\n" );
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document.write( "sum of squares = product of sum and diff + 8 becomes:\r<BR>\n" );
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document.write( "2^2 + 3^2 = 5 + 8 which becomes:\r<BR>\n" );
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document.write( "4 + 9 = 13\r<BR>\n" );
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document.write( "since this statement is true, the value for x is good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "the 2 consecutive numbers that will satisfy the problem statement are 2 and 3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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