document.write( "Question 850743: if the sum of the roots of quadratic equation, ax^2+bx+c=0, is equal to the sum of cubes of their reciprocals then show that ab^2=3a^2c+c^3 \n" ); document.write( "

Algebra.Com's Answer #512414 by AnlytcPhil(1806) $\"\"$ $\"About$

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Question 850743
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\n" ); document.write( "if the sum of the roots of quadratic equation, ax^2+bx+c=0, is equal to the sum of cubes of their reciprocals then show that ab^2=3a^2c+c^3
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document.write( "The sum of the roots of  is \r\n" );
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document.write( "Use the quadratic formula to find the sum of the cubes of the reciprocals of the roots:\r\n" );
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document.write( "To make things easier, let \r\n" );
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document.write( "Combine fractions on the left\r\n" );
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document.write( "Divide through by \r\n" );
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document.write( "The numerator factors as the sum of two cubes:\r\n" );
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document.write( "The denominator simplifies:\r\n" );
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document.write( "So we have\r\n" );
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document.write( "Since \r\n" );
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document.write( "Substitute for z˛\r\n" );
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document.write( "Simplify the fraction on the left \r\n" );
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document.write( "Divide both sides by -b\r\n" );
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document.write( "Multiply both sides by 8ał\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "Edwin

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