Question 6
a. Show that $x^4 - x^3 - x + 1 \ge 0$, for all real numbers $x$.
b. Find all real numbers $x_1, x_2$ and $x_3$ given that $x_1 + x_2 + x_3 = 3$ and $x_1^3 + x_2^3 + x_3^3 = x_1^4 + x_2^4 + x_3^4$.
b. Find all real numbers $x_1, x_2$ and $x_3$ given that $x_1 + x_2 + x_3 = 3$ and $x_1^3 + x_2^3 + x_3^3 = x_1^4 + x_2^4 + x_3^4$.