You should be able to solve this

Show me what ya got.

1) If f(x) + f\left(\frac{1}{1-x}\right) = x+1 for all x \ne 1, find a formula for f(x).

2) If a,b,c,d are distinct
numbers such that for some number k
a^4+a^2+ka+64=0
b^4+b^2+kb+64=0
c^4+c^2+kc+64=0
d^4+d^2+kd+64=0
find a^2 + b^2 + c^2 + d^2.

3) Let f be an infinitely differentiable function on [0,1).  Extend f to \mathbb{R^+} by defining f(x) = f(x-1) + f'(x-1) when x \ge 1.  Find a one term expression for f involving only elementary functions, the differentiation operator, the floor operator, and f evaluated on [0,1).

(inb4 the TeX's all fucked up)

>>10
>Where are these questions from?
If I told you that, you'd be able to look up the answers.

>>11
Wellllll, that's ONE way to do it I guess...  There's a MUCH simpler way that shouldn't involve Ferrari's formula or any computers or brute-force solving.

>>12
Yep, that's basically the idea.  Doesn't really matter what the actual answer is.  One down.

>>13
Going in the right direction, but the answer shouldn't have a sum in it.

(and ONE down, TWO to go, as far as I can see :P)