The equation f (x) 2+BF (x)+c = 0 about x has five different real roots x 1, x2, x3, x4, x5,

Then two unequal real roots of f(x) are needed. Combining the images of f(x), we can know that f(x)= 1 has three values for x, one of which is 2, the other two are symmetrical about x=2, and the sum is 4.

Another value of f(x) is a value other than 1. According to the image, it also corresponds to two values of x, which are symmetrical about x=2 and the sum is 4.

Therefore, x1+x2+x3+x4+X5 =10, f (x1+x2+x3+x4+X5) = f (10) = lg8 = 3lg2.