Problem 13

Explanation

We will analyze quantities $P$ and $Q$ separately.

Analyzing Quantity P

The expression for $P$ can be simplified as follows:

Given $0 < x < 1$. Thus:

Analyzing Quantity Q

Given $Q = 2+x$. Since $0 < x < 1$, then:

Comparing P and Q

From the analysis above, we have:

• $1 < P < 2$
• $2 < Q < 3$

It is clear that the maximum value of $P$ is less than the minimum value of $Q$.

Thus, $P < Q$.