Math Problem Statement

Giả sử x, y, z là những số thực lớn hơn 2. Tìm giá trị nhỏ nhất của biểu thức P = x / √(y + z - 4) + y / √(z + x - 4) + z / √(x + y - 4).

Solution

The image contains a mathematical expression that seems to be asking for the minimum value of the given function PP, where xx, yy, and zz are real numbers greater than 2. The expression for PP is:

P=xy+z4+yz+x4+zx+y4.P = \frac{x}{\sqrt{y + z - 4}} + \frac{y}{\sqrt{z + x - 4}} + \frac{z}{\sqrt{x + y - 4}}.

To find the minimum value of this expression, we can utilize optimization techniques such as partial derivatives or symmetry considerations, given the structure of the problem.

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Math Problem Analysis

Mathematical Concepts

Optimization
Partial Derivatives
Symmetry

Formulas

P = x / √(y + z - 4) + y / √(z + x - 4) + z / √(x + y - 4)

Theorems

Optimization techniques
Symmetry methods in optimization

Suitable Grade Level

Grades 11-12