Question 116
How many triples $(a,b,c)$ of real numbers satisfy the system
$$\begin{cases}a^2+b^2+c^2=1,\\a^3+b^3+c^3=1\end{cases}$$
(A) None
(B) 1
(C) 3
(D) 6
(E) Infinitely many.
$$\begin{cases}a^2+b^2+c^2=1,\\a^3+b^3+c^3=1\end{cases}$$
(A) None
(B) 1
(C) 3
(D) 6
(E) Infinitely many.