Math Problem Statement

Cho hai biểu thức A = √(x) / (x-2) và B = √(x) / (x-3) với x ≥ 0, x ≠ 2, x ≠ 3. 1) Tính giá trị của biểu thức A khi x = 25. 2) Chứng minh B = √(x) / (x+3). 3) Xét biểu thức P = A·B. Tìm tất cả các giá trị của x để P = (4x+3) / √(x-2).

Solution

The problem you've uploaded contains several mathematical tasks related to square roots. Here's a breakdown of the questions:

  1. Task 1: Calculate the value of the expression A=xx2A = \frac{\sqrt{x}}{x-2} when x=25x = 25.

  2. Task 2: Prove that B=xx+3B = \frac{\sqrt{x}}{x+3} holds.

  3. Task 3: Consider the expression P=ABP = A \cdot B. Find all the values of xx for which P=4x+3x2P = \frac{4x+3}{\sqrt{x-2}}.

Would you like me to work through the steps to solve these problems? Feel free to let me know if you need any further clarification!

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Math Problem Analysis

Mathematical Concepts

Square Roots
Algebraic Expressions
Equations

Formulas

A = √(x) / (x-2)
B = √(x) / (x-3)
P = A·B
P = (4x+3) / √(x-2)

Theorems

Simplification of algebraic expressions
Substitution method
Equality of expressions

Suitable Grade Level

Grades 9-11