Ta có : \(a^3-3ab^2=5\Rightarrow\left(a^3-3ab^2\right)^2\)\(=25\Rightarrow a^6-6a^4b^2+9a^2b^4=25\)
\(b^3-3a^2b=10\Rightarrow\left(b^3-3a^2b\right)^2=100\)\(\Rightarrow b^6-6a^2b^4+9a^4b^2=100\)
Cộng hai vế ta được :
\(a^6-6a^4b^2+9a^2b^4+b^6-6a^2b^4+9a^4b^2=125\)
\(\Rightarrow a^6+3a^4b^2+3a^2b^4+b^6=125\)
\(\Rightarrow\left(a^2+b^2\right)^3=125\)
\(\Rightarrow\left(a^2+b^2\right)^3=5^3\)
\(\Rightarrow a^2+b^2=5\)
\(\Rightarrow\frac{a^2+b^2}{2018}=\frac{5}{2018}\)
Chúc bạn học tốt ^^