x^3+2mx^2-3x= 2mx-2 \\ \\ (x-1)(x^2+(2m+1)x-2) = 0 \\ \\ A (1,2m-2) \\ \\ g(x) = x^2+(2m+1)x-2 = 0 \\ \\ dk: g(1) \not = 0 \Rightarrow m \not = 0 , \Delta > 0 \Rightarrow \forall m \in R \\ \\ x_1+x_2 = -2m-1 \\ \\ x_1x_2 =-2 \\ \\ B(x_1, 2mx_1-2) \\ \\ C(x_2,2mx_2-2) \\ \\ d(O, BC) =...