Troll problem :)

by junbeom01pd2020, Apr 11, 2017, 6:30 AM

source: Myself
Let the 100 roots of the equation \(x^{100}-5x+2=0\) be \(r_{1}, r_{2}, r_{3},\ldots, r_{100}\). Find \[ r_{1}^{100}+r_{2}^{100}+r_{3}^{100}+\cdots+r_{100}^{100} . \]
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Here's nice sol: Note that $r_i^{100}=5r_i-2$ so \[r_1^{100}+r_2^{100} + \ldots + r_{100}^{100} = 5(r_1+r_2+ \ldots + r_{100}) - 200\]but $r_1+r_2+\ldots + r_{100} = 0$ cause Vieta's so answer is $-200.$

by shiningsunnyday, Apr 11, 2017, 9:05 AM

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Alternatively

by pi_Plus_45x23, Apr 11, 2017, 11:57 AM

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EDIT: sniped xD

by pi_Plus_45x23, Apr 11, 2017, 11:57 AM

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