document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064107>Question 1064107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the smallest possible value for the product of<BR>\n" );
document.write( "2 real numbers that differ by 6?<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 #679150 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=679150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be the larger number<BR>\n" );
document.write( "the smaller number is therefore x-6.\r<BR>\n" );
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document.write( "the difference between the numbers will always be 6.\r<BR>\n" );
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document.write( "their product would be x * (x-6) = x^2 - 6x.\r<BR>\n" );
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document.write( "let y be their product and you get y = x^2 - 6x.\r<BR>\n" );
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document.write( "you can use the max/min value formula to get the value of x where y is either max or min.\r<BR>\n" );
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document.write( "since the coefficient of the x^2 term is positive, the max/min value will be min.\r<BR>\n" );
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document.write( "set y = 0 and the quadratic equation is in standard form of ax^2 + bx = 0\r<BR>\n" );
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document.write( "this means that a = 1 and b = 6.\r<BR>\n" );
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document.write( "the min/max formula for x is x = -b/2a.\r<BR>\n" );
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document.write( "you will get x = -b/2a which becomes x = 6/2 = 3.\r<BR>\n" );
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document.write( "when x = 3, the value of y is 9 - 18 = -9.\r<BR>\n" );
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document.write( "the minimum value of the product is therefore -9.\r<BR>\n" );
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document.write( "here is a graph of the quadratic equation in standard form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-12%2C12%2C-12%2C12%2Cx%5E2+-+6x%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-12%2C12%2C-12%2C12%2Cx%5E2+-+6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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