If \( \alpha, \beta \neq 0 \) and \( f(n)=\alpha^{n}+\beta^{n} \) a...
If \( \alpha, \beta \neq 0 \) and \( f(n)=\alpha^{n}+\beta^{n} \) and \( \left|\begin{array}{ccc}3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4)\end{array}\right|=K(1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2} \), then \( K \) is equal
\( \mathrm{P} \) to
(1) 1
(2) -1
(3) \( \alpha \beta \)
(4) \( \frac{1}{\alpha \beta} \)
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