Let \(n \ge 2\) be a positive integer. The equation \(nx^{n - 1} + (n - 1) x^{n - 2} + \dots + 3x^2 + 2x + 1 = n^2\) has a rational root between 1 and 2. Find this rational root in terms of n. Thanks!
The rational root is (n + 1)^2/n.
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