document.write( "Question 1203032: Determine the value of k such that the trinomial 4x^2-kx+81 is a perfect square (such as (ax+b)^2. \n" ); document.write( "

Algebra.Com's Answer #838263 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "We write  4x^2 - kx + 81 = .\r\n" );
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document.write( "It gives us  4x^2 - kx + 81 = a^2*x^2 + 2abx + b^2.\r\n" );
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document.write( "From this, we conclude that either\r\n" );
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document.write( "    (a)  a = 2, b = 9,\r\n" );
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document.write( "or\r\n" );
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document.write( "    (b)  a = -2, b = 9,\r\n" );
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document.write( "or\r\n" );
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document.write( "    (c)  a = 2, b = -9\r\n" );
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document.write( "or\r\n" );
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document.write( "    (d)  a = -2, b = -9.\r\n" );
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document.write( "It gives for \"k\" two and only two opportunities: either k = 2ab = 36  or  k = 2ab = -36.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be attentive: the problem INCORRECTLY asks about \"the value of k\",
\n" ); document.write( "while a correct question must be \"find all possible values of k\".\r
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\n" ); document.write( "\n" ); document.write( "So, the problem's formulation has a huge underwater stone (is a trap),
\n" ); document.write( "expecting you will fall in it.\r
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