f(x)=1xx+12xx(x-1)x(x+1)3x(x-1)x(x-1)(x-2)(x-1)x(x+1)⇒f(2012)=

Solution:

$f (x) =$ $|\begin{array}{lcc} 1 & x & x + 1 \\ 2 x & x (x - 1) & x (x + 1) \\ 3 x (x - 1) & x (x - 1) (x - 2) & (x - 1) x (x + 1) \end{array}|$

$f (x) = x^{2} (x - 1) (x + 1)$ $|\begin{array}{lcc} 1 & x & 1 \\ 2 & (x - 1) & 1 \\ 3 & (x - 2) & 1 \end{array}|$
$R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}$

$f (x) = x^{2} (x - 1) (x + 1)$ $|\begin{array}{lcc} 1 & x & 1 \\ 1 & - 1 & 0 \\ 2 & - 2 & 0 \end{array}| = 0$

$f (x) =$ $|\begin{matrix} 1 & x & x + 1 \\ 2 x & x (x - 1) & x (x + 1) \\ 3 x (x - 1) & x (x - 1) (x - 2) & (x - 1) x (x + 1) \end{matrix}|$ $\Rightarrow f (2012) =$

Solution:

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