Đáp án:
\(\left[ \begin{array}{l}
{x^5} - {y^5} = - 242\\
{x^5} - {y^5} = 242
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x + y = 4\\
xy = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 4 - y\\
\left( {4 - y} \right)y = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 4 - y\\
4y - {y^2} - 3 = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 4 - y\\
\left[ \begin{array}{l}
y = 3\\
y = 1
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1\\
x = 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^5} - {y^5} = 1 - {3^5} = - 242\\
{x^5} - {y^5} = {3^5} - 1 = 242
\end{array} \right.
\end{array}\)
