document.write( "Question 1209228: Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = -3x^2 + 15x + 11. Compute 1/a^2 + 1/b^2. \n" ); document.write( "

Algebra.Com's Answer #847874 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = -3x^2 + 15x + 11.
\n" ); document.write( "Compute 1/a^2 + 1/b^2.
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document.write( "This given equation is reduced to the standard form quadratic equation\r\n" );
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document.write( "    5x^2 - 23x - 4 = 0.    (1)\r\n" );
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document.write( "Therefore, according to Vieta's theorem,  \r\n" );
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document.write( "    a + b = ,    (2)\r\n" );
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document.write( "    ab = .       (3)\r\n" );
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document.write( "Next,  \r\n" );
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document.write( "     +  = .    (4)\r\n" );
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document.write( "The numerator in (4) is\r\n" );
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document.write( "    a^2 + b^2 = (a^2 + 2ab + b^2) - 2ab = (a+b)^2 - 2ab = \r\n" );
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document.write( "                replace here a+b by   and replace ab by    based on (2),(3) and continue\r\n" );
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document.write( "              =  -  =  +  =  = .\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "     +  =  =  =  = 35 = 35.5625.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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