document.write( "Question 1039518: a^2 +b^2 +2b +4a +5=0, then the value of
\n" ); document.write( " $\"%28a-b%29%2F%28a%2Bb%29\"$ is _____. Explain clearly\r
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\n" ); document.write( "d)-1/3 \n" ); document.write( "

Algebra.Com's Answer #654311 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "a² + b² + 2b + 4a + 5 = 0\r\n" );
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document.write( "We want to know what values a and b will have to be in order\r\n" );
document.write( "for a and b to be real numbers and not imaginary numbers.\r\n" );
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document.write( "Write as a quadratic in \"a\":\r\n" );
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document.write( "a² + 4a + (b²+2b+5) = 0\r\n" );
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document.write( "In order to have real solutions, the discriminant of a \r\n" );
document.write( "quadratic must not be negative.\r\n" );
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document.write( "The discriminant is B²-4AC (Using capital letters to avoid\r\n" );
document.write( "conflict of notation with small letters)\r\n" );
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document.write( "A = 1, B = 4, C = (b²+2b+5)\r\n" );
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document.write( "Discriminant = B²-4AC = 4²-4(1)(b²+2b+5) = 16-4(b²+2b+5) = \r\n" );
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document.write( "16-4b²-8b-20 = -4b²-8b-4 = -4(b²+2b+1) = -4(b+1)²\r\n" );
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document.write( "This must not be negative, so the only value it can take on\r\n" );
document.write( "so that -4(b+1)² is not negative is when it is zero.\r\n" );
document.write( "which is when b+1=0 or b=-1, so b can only be -1.  So b=-1.\r\n" );
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document.write( "That makes the original equation:\r\n" );
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document.write( "a² + b² + 2b + 4a + 5 = 0\r\n" );
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document.write( "become\r\n" );
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document.write( "a² + (-1)² + 2(-1) + 4a + 5 = 0\r\n" );
document.write( "        a² + 1 - 2 + 4a + 5 = 0\r\n" );
document.write( "                a² + 4a + 4 = 0\r\n" );
document.write( "                     (a+2)² = 0\r\n" );
document.write( "                        a+2 = 0\r\n" );
document.write( "                          a = -2\r\n" );
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document.write( "So since a=-2 and b=-1\r\n" );
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document.write( "Edwin

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