Math Problem Statement

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.

Solution

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 α\alpha and β\beta, with the condition that: α+β=9\alpha + \beta = 9

  • There's a second equation involving α\alpha and β\beta in a floor function: 2α=x22 \left\lfloor \alpha \right\rfloor = \left\lfloor x^2 \right\rfloor

  • The task is to find which number could be represented by: αβ\left\lfloor \alpha \right\rfloor - \left\lfloor \beta \right\rfloor

The options are given as:

  1. 11
  2. 22
  3. 44
  4. 66
  5. 88

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Math Problem Analysis

Mathematical Concepts

Algebra
Floor Function

Formulas

α + β = 9
2 ⌊α⌋ = ⌊x^2⌋
⌊α⌋ - ⌊β⌋

Theorems

Properties of Floor Functions

Suitable Grade Level

Grades 9-12