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Find the range of r - ILL 1990 PRK1

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September 18, 2010
algebra proposedalgebra

Problem Statement

Let a+bia + bi and c+dic + di be two roots of the equation xn=1990x^n = 1990, where n≥3n \geq 3 is an integer and a,b,c,d∈Ra,b,c,d \in \mathbb R. Under the linear transformation f=(acbd)f =\left(\begin{array}{cc}a&c\\b &d\end{array}\right), we have (2,1)→(1,2)(2, 1) \to (1, 2). Denote rr to be the distance from the image of (2,2)(2, 2) to the origin. Find the range of r.r.
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