https://file.aiquickdraw.com/mathbot/file/1728963835981p3kcw1se.jpg

The image shows a math problem written in Persian script with a mix of mathematical notation and equations. Here's an English interpretation of the problem:

- We have two variables \(\alpha\) and \(\beta\), with the condition that:
  \[
  \alpha + \beta = 9
  \]
  
- There's a second equation involving \(\alpha\) and \(\beta\) in a floor function:
  \[
  2 \left\lfloor \alpha \right\rfloor = \left\lfloor x^2 \right\rfloor
  \]
  
- The task is to find which number could be represented by:
  \[
  \left\lfloor \alpha \right\rfloor - \left\lfloor \beta \right\rfloor
  \]
  
The options are given as:
  1. \(1\)
  2. \(2\)
  3. \(4\)
  4. \(6\)
  5. \(8\)

Would you like me to go step by step to explain how to solve this?

We have two variables α and β with α + β = 9. Also, 2 ⌊α⌋ = ⌊x^2⌋. Find the possible value of ⌊α⌋ - ⌊β⌋ from the given options.

Explore how to solve an algebraic system with floor functions and variables. The problem involves finding possible values of ⌊α⌋ - ⌊β⌋ under the condition α + β = 9, using floor function properties and algebra. Suitable for Grades 9-12.

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