Question 87
Given nonzero real numbers $a, b, c$, with
$$
a + b + c = a^2 + b^2 + c^2 = a^3 + b^3 + c^3. \quad (*)
$$
a) Find $\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) (a + b + c - 2)$.
b) Do there exist pairwise different nonzero $a, b, c$ satisfying $(*)$?
(D. Bazylev)
$$
a + b + c = a^2 + b^2 + c^2 = a^3 + b^3 + c^3. \quad (*)
$$
a) Find $\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) (a + b + c - 2)$.
b) Do there exist pairwise different nonzero $a, b, c$ satisfying $(*)$?
(D. Bazylev)