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What is the sum of the squares of roots of the equation below?

$m^{1/3} + ( 2m-3)^{1/3} = \big(12 ( m – 1)\big)^{1/3}$

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    The sum of squares of the roots of $x^3+a x^2+b x + c$ is $a^2 - 2b$.2012-02-23

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Call the roots $a,b,c$. From the equation in your comment, do you know how to get $a+b+c$? do you know how to get $ab+ac+bc$? can you work out how to get $a^2+b^2+c^2$, if you know $a+b+c$ and $ab+ac+bc$?

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    Do you have some reason to think the answer is an integer?2012-02-23