Question 2
a) Prove that $x^4-x^3-x+1\ge0$ for every real $x$.
b) Solve over the reals:
$$\begin{cases}x_1+x_2+x_3=3,\\x_1^3+x_2^3+x_3^3=x_1^4+x_2^4+x_3^4.\end{cases}$$
b) Solve over the reals:
$$\begin{cases}x_1+x_2+x_3=3,\\x_1^3+x_2^3+x_3^3=x_1^4+x_2^4+x_3^4.\end{cases}$$