document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66038>Question 66038</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/093979862x/algebrahomeworkh>an incremental development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> find three consectuitve intergers such that twice the product of the first and second exceeds the square of the third by 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46749 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> QUESTION:\r<BR>\n" );
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document.write( "find three consectuitve intergers such that twice the product of the first and second exceeds the square of the third by 4\r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "Here we have three consecutive numbers.....\r<BR>\n" );
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document.write( "So we can take three consecutive numbers as (x-1), x , (x+1)\r<BR>\n" );
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document.write( "Product of first and second is (x-1)*x = x^2 - x\r<BR>\n" );
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document.write( "Twice the Product of first and second is = 2(x^2 - x )\r<BR>\n" );
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document.write( "==>    = 2x^2 - 2x \r<BR>\n" );
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document.write( "Now square of the third is = (x+1)^2\r<BR>\n" );
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document.write( "==> x^2 + 2x + 1\r<BR>\n" );
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document.write( "according to the question,... twice the product of the first and second exceeds the square of the third by 4\r<BR>\n" );
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document.write( "which implies.....\r<BR>\n" );
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document.write( "2x^2 - 2x = x^2 + 2x + 1 + 4 ( exceeds 4 means + 4 )\r<BR>\n" );
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document.write( "==> 2x^2 - 2x = x^2 + 2x + 5\r<BR>\n" );
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document.write( "subtract x^2 from bioth sides of the expression...\r<BR>\n" );
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document.write( "==>2x^2 - 2x - x^2 = x^2 + 2x + 5 -x^2\r<BR>\n" );
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document.write( "==> x^2 - 2x  = 2x + 5\r<BR>\n" );
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document.write( "Subtract 2x from both sides....\r<BR>\n" );
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document.write( "==> x^2 - 2x - 2x = 2x + 5 - 2x\r<BR>\n" );
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document.write( "==> x^2 - 4x = 5\r<BR>\n" );
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document.write( "Again subtract 5 from both sides....\r<BR>\n" );
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document.write( "==> x^2 - 4x  - 5 = 5 - 5\r<BR>\n" );
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document.write( "==> x^2 - 4x  - 5 = 0\r<BR>\n" );
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document.write( "Here we have quadratic equation...Solve this function to get the value of \"x\"\r<BR>\n" );
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document.write( "Here we use the  following method ,....\r<BR>\n" );
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document.write( "GFind two numbers such that whose sum is -4 and whose product is -5\r<BR>\n" );
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document.write( "Such two numbers are -5 and +1\r<BR>\n" );
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document.write( "So we can write the above equation as ....\r<BR>\n" );
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document.write( "x^2 - 5x + 1x - 5 = 0 ( split the middle term only)\r<BR>\n" );
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document.write( "(x^2 - 5x ) + (1x - 5 )= 0\r<BR>\n" );
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document.write( "==> x ( x - 5 ) + 1( x - 5) = 0\r<BR>\n" );
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document.write( "==> ( x- 5)(x + 1 ) = 0\r<BR>\n" );
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document.write( "==> either ( x- 5)= 0 or (x + 1 ) =0\r<BR>\n" );
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document.write( "( x- 5)= 0 ==> x = 5 and \r<BR>\n" );
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document.write( "(x + 1 )= 0 ==> x = -1\r<BR>\n" );
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document.write( "So we have two values for x that is 5 and -1\r<BR>\n" );
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document.write( "If x = 5,  then  numbers are (5-1), 5, (5+1)\r<BR>\n" );
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document.write( "That is 4,5 and 6\r<BR>\n" );
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document.write( "If we take x = -1, then the numbers are (-1-1), -1, (-1+1)\r<BR>\n" );
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document.write( "That is -2, -1 and 0\r<BR>\n" );
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document.write( "Hope you understood...\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "praseena.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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