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Resuelve La siguiente pirámide algebraica con los datos proporcionados

To solve the algebraic pyramid shown in the image, we need to understand that each block in the pyramid is typically the sum of the two blocks directly below it. This rule is generally followed for such puzzles unless stated otherwise.

Given the numbers:

- Top row: 738
- Second row: 218 and 112
- Third row: (empty blocks)
- Fourth row: 45 and 7

Let’s denote the unknown blocks from left to right in the third row as \( x_1 \), \( x_2 \), and \( x_3 \), and the blocks in the fourth row from left to right as \( x_4 \), \( x_5 \), and \( x_6 \).

Using the sum rule:

1. **For the top block**:
   \[
   738 = 218 + 112 + x_1
   \]
   This simplifies to:
   \[
   x_1 = 738 - 218 - 112 = 408
   \]

2. **For the second row (left block)**:
   \[
   218 = x_4 + x_5
   \]

3. **For the second row (right block)**:
   \[
   112 = x_5 + x_6
   \]

4. **For the third row**:
   \[
   x_4 = 45 \quad \text{and} \quad x_6 = 7
   \]

Substitute \( x_4 \) and \( x_6 \) into the above equations:

- \( 218 = 45 + x_5 \)  → \( x_5 = 218 - 45 = 173 \)
- \( 112 = 173 + 7 \)   → This holds true, so we have our numbers.

Thus, the pyramid should be filled as follows:

- **Fourth row**: \( 45 \), \( 173 \), \( 7 \)
- **Third row**: \( 218 \), \( 112 \)
- **Second row**: \( 408 \)
- **Top**: \( 738 \)

Would you like further details or explanations on this solution?

Here are some related questions you might consider:

1. How would you approach this problem if the pyramid rule was different (e.g., subtraction instead of addition)?
2. Can you create a similar pyramid using different initial values?
3. What if the numbers in the pyramid had to satisfy a different mathematical property, such as multiplication?
4. How can algebraic methods be used to solve pyramids with larger or more complex structures?
5. What other patterns or sequences can be used to create mathematical pyramids?

**Tip:** Always verify each step when solving pyramid problems to ensure that the sum rule is applied consistently across all levels.

Aprende cómo resolver la pirámide algebraica dada con una solución detallada paso a paso. Este problema cubre conceptos algebraicos clave y es adecuado para estudiantes de los grados 7-9.

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