a: \(a^2+b^2=\left(a+b\right)^2-2ab=25-12=13\)
\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\)
\(=-125-3\cdot6\cdot\left(-5\right)=-125+90=-35\)
c: \(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)
\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)