Math Problem Statement

Solución del problema

Solution

The image shows a mathematical problem that asks for the solution to a system of equations. The specific problem seems to require identifying one of the values of xx in the equation given.

The key part of the problem appears to be the square root expression:

2x5x=2\sqrt{\frac{2x - 5}{x}} = 2

To solve for xx, we can proceed as follows:

  1. Square both sides to eliminate the square root:

    (2x5x)2=22\left(\sqrt{\frac{2x - 5}{x}}\right)^2 = 2^2

    This simplifies to:

    2x5x=4\frac{2x - 5}{x} = 4

  2. Multiply both sides by xx to eliminate the fraction:

    2x5=4x2x - 5 = 4x

  3. Rearrange the equation to solve for xx:

    2x4x=52x - 4x = 5

    Simplifying further:

    2x=5-2x = 5

    So:

    x=52x = -\frac{5}{2}

This value does not appear directly in the options given, so it may be necessary to check for extraneous solutions or consider any other constraints implied by the problem.

Since the problem asks for "uno de los valores de xx," and considering possible integer results from the original equation after checking the steps, the correct answer is not explicitly clear based on this calculation alone. However, typically, such problems expect integer results.

Would you like a more detailed check or further exploration of the system?


Relative Questions:

  1. What happens if you substitute x=52x = -\frac{5}{2} back into the original equation?
  2. Are there any other methods to solve this equation that might give an integer value for xx?
  3. Could there be a mistake in interpreting the equation from the problem statement?
  4. What are the other types of solutions or possible interpretations of this problem?
  5. How would the answer change if the equation were different?

Tip: Always check your solutions by substituting them back into the original equation to ensure they satisfy the conditions given.

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Math Problem Analysis

Mathematical Concepts

Equations
Square Roots
Algebra

Formulas

Square root property
Equation solving techniques

Theorems

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Suitable Grade Level

Grades 9-12