Roots of Equation: Sum of Fourth Powers | Math Homework

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To find the sum of the fourth powers of the roots of the equation x^3 + x + 1 = 0, a more efficient method is desired instead of lengthy calculations. Participants discuss various approaches, seeking a formulaic solution that simplifies the process. The conversation highlights the need for a quicker technique to avoid time-consuming methods. Ultimately, the focus remains on finding an optimal solution for calculating the sum of the fourth powers of the roots. A concise and effective method is sought to streamline the problem-solving process.
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Homework Statement



The sum of the fourth powers of the roots of the equation x3+x+1=0 is?

The Attempt at a Solution



Is there any shortest method to find out the answer using some formulae? I know a method but its very very lengthy and time consuming.
 
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Is it this method you know or another method?
 
I was just looking for that. Thank you so much!
 

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