F(x) is meaningful, then the solution set of the inequality about t is 1+t+at 2 > 0 contains (0,2).

So a & gt-(t+ 1)/t 2 remains (0,2).

Since-(t+1)/t2 =-1/t-1/t2 is the increasing function on (0,2), the maximum value is-(2+1)/2 2 =-3/.

So a & gt-3/4.

20. Because the function is an even function, f(-x)-f(x)=0 holds.

That is, LG [10 (-x)+1]+a (-x)-LG (10x+1)-ax = 0 holds.

Therefore, LG [(10x+1)10x]-LG (10x+1) = 2ax holds.

That is, LG (110x) = 2ax holds.

That is, -x=2ax holds,

Then 2a=-1,

So a=-1/2.

2 1, 9+(3x-1) = 3x * (3x-1) After denominator division,

Let t = 3 x > 0 and the equation is t 2-2t-8 = 0.

Decomposition to (t+2)(t-4)=0,

The solution is t=4 (minus 2),

That is 3 x = 4,

So x=log3(4).