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Let \(x_1, \dots, x_n \in \mathbb{K}\) be pairwise distinct and \(L_1, \dots, L_n\) the associated Lagrange polynomials. Show that $$ \sum_{i=1}^{n} L_i(X) = 1 \quad \text{(constant polynomial)}. $$ Hint. Apply the Lagrange identity of the previous exercise to a particular \(P\).
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