How much of this do you need to do by hand?
Well here is a relevant graph
https://www.desmos.com/calculator/mtrfxxuwrs
I can see from the graph that y=x
$${{\mathtt{x}}}^{{\mathtt{6}}}{\mathtt{\,-\,}}{{\mathtt{x}}}^{{\mathtt{4}}} = {\mathtt{18}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{3}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{3}}}}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\sqrt{{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{\,-\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{\,-\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
\end{array} \right\}$$
so the real solutions are
$$(-\sqrt3,-\sqrt3),\quad (\sqrt3,-\sqrt3),\quad (-\sqrt3,\sqrt3),\quad and \quad (\sqrt3,\sqrt3)$$
NOW how much of this did you really need to do by hand?
so this is as far as I got... And btw the question is Find all pairs of real numbers I don't know if i translate that good because English isn't my native language...
How much of this do you need to do by hand?
Well here is a relevant graph
https://www.desmos.com/calculator/mtrfxxuwrs
I can see from the graph that y=x
$${{\mathtt{x}}}^{{\mathtt{6}}}{\mathtt{\,-\,}}{{\mathtt{x}}}^{{\mathtt{4}}} = {\mathtt{18}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{3}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{3}}}}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\sqrt{{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{\,-\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{\,-\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}}}\\
\end{array} \right\}$$
so the real solutions are
$$(-\sqrt3,-\sqrt3),\quad (\sqrt3,-\sqrt3),\quad (-\sqrt3,\sqrt3),\quad and \quad (\sqrt3,\sqrt3)$$
NOW how much of this did you really need to do by hand?