Excel in math, science, and engineering

\[ \large x \ln x + y \ln y + z \ln z \]

Let \(x,y\) and \(z\) be positive numbers satisfying \(x+y + z= 3e\).

Find the minimum value of the expression ...

Which area is larger?

How many integer solutions are there to

\[ x^y = y^ x, x \neq y ? \]

For inspiration, see report.

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