Find two positive numbers x and y such that their sum is 35 and the product `x^2y^5`is a maximum.

Explanation

To solve the problem of finding two positive numbers \( x \) and \( y \) such that their sum is 35 and the product \( P = x^2 y^5 \) is maximized, we can follow these steps:

### Step 1: Set up the equations
We know from the problem that:
\[ x + y = 35 \]
We can express \( y \) in terms of \( x \):
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