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Help for II-A Algebra 9.18

 
 
LuFiona的头像
Help for II-A Algebra 9.18
LuFiona - 2019年08月6日 Tuesday 22:29
 

Questions 9.18 is Find the sum of the 55th powers of the 55 roots of x5+2x−1=0x5+2x−1=0.

Currently, I'm having trouble figuring out how to use different groupings of the roots (taken by 2, taken by 3, etc.) to isolate the fifth powers of the roots. 

Does anyone have any good hints or help for this problem?

 
ReynosoDavid的头像
Re: Help for II-A Algebra 9.18
ReynosoDavid - 2019年08月12日 Monday 13:17
 

Since all five roots of $x^5 + 2x -1 = 0$ satisfy the equation, for each of them we have that $x_{k}^5 = -2x_{k} + 1$, ($k=1,2,3,4,5$). Using this, what is $x_{1}^5 + x_{2}^5 + x_{3}^5 + x_{4}^5 + x_{5}^5$ equal to?

 
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