https://r2.erweima.ai/mathbot/image/1726895904581szvidvto.jpg

The image contains a mathematical expression and a problem written in Persian. The main equation in the image appears to be:

\[
\sqrt{1 - x} + \sqrt{x - 1} = a
\]

The Persian text asks a question about the values of \( \alpha \) and \( \beta \) with the following expression:

\[
\text{If } \alpha \text{ and } \beta \text{ are } \dots, \quad \frac{\alpha}{12} + \frac{\beta}{12} = \dots ?
\]

To fully interpret this question and provide a solution, I need more context about what \( \alpha \) and \( \beta \) represent, as well as what the problem is asking for.

Would you like me to proceed with solving the equation \( \sqrt{1 - x} + \sqrt{x - 1} = a \), or would you like further clarification on the Persian text?

Let me know how you'd like to proceed!

Here are 5 follow-up questions to expand your understanding:
1. What values of \( a \) make the equation \( \sqrt{1 - x} + \sqrt{x - 1} = a \) valid?
2. How can we define the domain of the function involving square roots?
3. Are there any specific solutions for \( x \) that satisfy the equation based on the value of \( a \)?
4. How would this problem change if we modified the constants inside the square roots?
5. What techniques are used to simplify equations with square roots on both sides?

**Tip:** Always check the domain of a function involving square roots, since they are only defined for non-negative values.

Solve the equation involving square roots: √(1 - x) + √(x - 1) = a. Also, interpret the question involving α and β: If α and β are ..., what is (α/12) + (β/12)?

Learn how to solve the equation √(1 - x) + √(x - 1) = a and interpret expressions involving α and β. This problem covers square roots and algebraic concepts. Suitable for students in Grades 10-12.

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