It is known that the odd function f (x) defined on R satisfies f (x-4) = - f (x) and is an increasing function in the interval [0,2]. If the equation f (x) = m (M > 0) has four different roots x1, X2, X3, X4 in the interval [- 8,8], then X1 + x2 + X3 + X4 =

It is known that the odd function f (x) defined on R satisfies f (x-4) = - f (x) and is an increasing function in the interval [0,2]. If the equation f (x) = m (M > 0) has four different roots x1, X2, X3, X4 in the interval [- 8,8], then X1 + x2 + X3 + X4 =

Increasing function on [0,2] is symmetric about the origin
So it decreases on [- 2,0]
F (x-4) = - f (x) indicates that the sign of F (x) should be changed once for every 4 f (x) difference of X
The length of [- 2,2] is 4
You can draw the rest
The answer is - 12 + 4 = - 8