Question 76
a) Prove that $x^2 + x + 1 \gt 0$ and $x^4 + x^3 + x^2 + x + 1 \gt 0$, for every real number $x$.
b) Find all real triples $(a, b, c)$ so that $a^8 + b^8 + c^8 = a^3 + b^3 + c^3$ and $a^5 + b^5 + c^5 = 3$.
b) Find all real triples $(a, b, c)$ so that $a^8 + b^8 + c^8 = a^3 + b^3 + c^3$ and $a^5 + b^5 + c^5 = 3$.