\(\begin{array}{l}
\left\{ \begin{array}{l}
x + y = 12\\
xy = 32
\end{array} \right.\\
a)\,{\left( {x - y} \right)^2} = {x^2} + {y^2} - 2xy = {x^2} + {y^2} + 2xy - 4xy\\
= {\left( {x + y} \right)^2} - 4xy = {12^2} - 4.32 = 16\\
\Rightarrow \left[ \begin{array}{l}
x - y = 4\\
x - y = - 4
\end{array} \right.\\
b)\,{\left( {x + y} \right)^2} = 144\\
\Leftrightarrow {x^2} + {y^2} + 2xy = 144\\
\Leftrightarrow {x^2} + {y^2} = 144 - 2.32\\
\Leftrightarrow {x^2} + {y^2} = 80\\
c)\,{x^3} + {y^3} = \left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right)\\
= 12\left( {80 - 2.32} \right)\\
= 12.16\\
= 192
\end{array}\)
