There is a system of equations ∗x+∗y+∗z=0,∗x+∗y+∗z=0,∗x+∗y+∗z=0. Two people alternately enter a number instead of a star. Prove that the player that goes first can always ensure that the system has a non-zero solution.
Find all functions f(x) defined for all real values of x and satisfying the equation 2f(x)+f(1−x)=x2.