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Consider the equation
x7+x6+x5+x4+x3+x2+x+1=0.x^7+x^6+x^5+x^4+x^3+x^2+x+1=0.x7+x6+x5+x4+x3+x2+x+1=0.
Let xkx_kxk be the kthk^\text{th}kth distinct root of the equation, and let ℜ(xk)\Re(x_k)ℜ(xk) be the real part of that root. Then
∑k=17[ℜ(xk)]2= ?\sum_{k=1}^7{\big[\Re(x_k)\big]^2}=\, ?k=1∑7[ℜ(xk)]2=?
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