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The question you're asking is written in Uzbek and involves solving an equation \( x^8 + ax^4 + 1 = 0 \). The problem asks to find the sum of all the roots of the equation, where the roots are structured to form an arithmetic progression.

### Steps to Solve:
The equation \( x^8 + ax^4 + 1 = 0 \) can be rewritten by using a substitution:
- Let \( y = x^4 \), which turns the equation into a quadratic:
  \[
  y^2 + ay + 1 = 0
  \]
  Solving this quadratic using the quadratic formula:
  \[
  y = \frac{-a \pm \sqrt{a^2 - 4}}{2}
  \]
- After solving for \( y \), we need to take square roots to find \( x \), since \( y = x^4 \).

The problem states that the roots form an arithmetic progression, and you are asked to find the sum of all roots. 

Would you like more details on solving this equation step-by-step or an explanation of the arithmetic progression aspect of the roots?

Here are 5 relative questions to consider:
1. How do we use the properties of an arithmetic progression to simplify the solution?
2. What does the structure of the equation \( x^8 + ax^4 + 1 = 0 \) tell us about its symmetry?
3. How does the sum of the roots change if we modify the parameter \( a \)?
4. What is the significance of the discriminant \( a^2 - 4 \) in the quadratic equation?
5. Can the roots of this equation be real, or are they complex?

**Tip:** When dealing with higher-degree polynomials, always look for potential substitutions that can reduce the degree of the equation to make it more solvable.

x^8 + ax^4 + 1 = 0 tenglama arifmetik progressiya tashkil qiluvchi 4 ta ildizlarga ega bo'ladi. Ularning yig'indisini toping.

Solve the polynomial equation x^8 + ax^4 + 1 = 0, where the roots form an arithmetic progression. This detailed solution involves algebraic techniques, quadratic equations, and properties of arithmetic progression. Suitable for students in Grades 9-12.

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