[tex] f = x^3-2x^2-2x+1\\ \\ x_1+x_2+x_3 = -(-2) = 2\\ \\ x_2+x_3 = 2-x_1\\ x_3+x_1 = 2-x_2\\ x_1+x_2 = 2-x_3 \\ \\ (x_2+x_3)(x_3+x_1)(x_1+x_2) =\\ = (2-x_1)(2-x_2)(2-x_3) \\ \\ f(x) = (x-x_1)(x-x_2)(x-x_3)\\ f(2) = (2-x_1)(2-x_2)(2-x_3) = \\ =2^3-2\cdot 2^2 - 2\cdot 2+1 =\\ = 8-8-4+1 = -3 \\ \\ \Rightarrow \boxed{ (x_2+x_3)(x_3+x_1)(x_1+x_2) = -3}[/tex]
