Problem

Source: Kosovo MO 2019 Grade 12, Problem 1

Tags: algebra



Does there exist a triangle with length $a,b,c$ such that: a) $\begin{cases} a+b+c=6 \\ a^2+b^2+c^2=13 \\ a^3+b^3+c^3=28 \end{cases}$ b) $\begin{cases} a+b+c=6 \\ a^2+b^2+c^2=13 \\ a^3+b^3+c^3=30 \end{cases}$