Find the number of ordered triples $(x,y,z)$ of real numbers such that
\begin{align*}
x + 2y + 4z &= 12, \\
xy + 2xz + 4yz &= 22, \\
xyz &= 6.
\end{align*}
Question:
Find the number of ordered triples $(x,y,z)$ of real numbers such that
\begin{align*}
x + 2y + 4z &= 12, \\
xy + 2xz + 4yz &= 22, \\
xyz &= 6.
\end{align*}
Answer:
Let's think step by step.

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6
Find the number of ordered triples $(x,y,z)$ of real numbers such that
\begin{align*}
x + 2y + 4z &= 12, \\
xy + 2xz + 4yz &= 22, \\
xyz &= 6.
\end{align*}
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