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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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I tried to solve it . But the equation become very complicated . 729m^3 - 2727m^2 + 3294m -1331 = 0 . –  vikiiii Feb 23 '12 at 10:49
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The sum of squares of the roots of $x^3+a x^2+b x + c$ is $a^2 - 2b$. –  WimC Feb 23 '12 at 10:54

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up vote 2 down vote accepted

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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Thabks Gerry.Got your answer. But the value is not coming as integer. I think i have done the solution wrong. –  vikiiii Feb 23 '12 at 10:59
    
Do you have some reason to think the answer is an integer? –  Gerry Myerson Feb 23 '12 at 11:09
    
Thanks Gerry . Its done. –  vikiiii Feb 23 '12 at 11:10

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