\(a^3-3ab^2=19\Rightarrow\left(a^3-3ab^2\right)^2=361\)

\(\Leftrightarrow a^6-6a^4b^2+9a^2b^4=361\left(1\right)\)

\(b^3-3a^2b=98\Rightarrow\left(b^3-3a^2b\right)^2=9604\)

\(\Leftrightarrow b^6-6a^2b^4+9a^4b^2=9604\left(2\right)\)

\(\text{Công 2 vế (1) và (2) ta được :}\)

\(a^6-6a^4b^2+9a^2b^4+b^6-6a^2b^4+9a^4b^2=9956\)

\(\Leftrightarrow a^6+3a^4b^2+3a^2b^4+b^6=9956\)

\(\Leftrightarrow\left(a^2+b^2\right)^3=9956\)

\(\Leftrightarrow a^2+b^2=\sqrt[3]{9956}\)

tu lam 

Ta có: \(\left\{{}\begin{matrix}a^3-3ab^2=19\\b^3-3a^2b=98\end{matrix}\right.\) => \(\left\{{}\begin{matrix}\left(a^3-3ab^2\right)^2=19^2=361\\\left(b^3-3a^2b\right)^2=98^2=9604\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}a^6-6a^4b^2+9a^2b^4=361\\b^6-6a^2b^4+9a^4b^2=9604\end{matrix}\right.\)

=> \(a^6+b^6+\left(9a^2b^4-6a^2b^4\right)+\left(9b^2a^4-6a^4b^2\right)=9965\)

=> \(a^6+3a^2b^4+3a^4b^2+b^6=9965\)

=> \(\left(a^2+b^2\right)^3=9965\)

=> \(a^2+b^2=\sqrt[3]{9965}\)