https://r2.erweima.ai/mathbot/image/1726459279866qikfsjwz.jpg

The problem states:

Given that \( a - b = b - c = 3 \), calculate the value of:

\[
T = \frac{(a - b)^2 + (b - c)^2 + (a - c)^2}{18}
\]

### Step-by-Step Solution:

1. **Analyze the given information:**
   \[
   a - b = b - c = 3
   \]
   This implies:
   \[
   a - b = 3 \quad \text{and} \quad b - c = 3
   \]
   Adding the two equations:
   \[
   (a - b) + (b - c) = a - c = 6
   \]
   Therefore:
   \[
   a - c = 6
   \]

2. **Substitute the values into the expression for \( T \):**

   \[
   T = \frac{(a - b)^2 + (b - c)^2 + (a - c)^2}{18}
   \]
   Using the values \( a - b = 3 \), \( b - c = 3 \), and \( a - c = 6 \), we substitute into the equation:
   \[
   T = \frac{3^2 + 3^2 + 6^2}{18}
   \]
   Simplifying the squares:
   \[
   T = \frac{9 + 9 + 36}{18} = \frac{54}{18} = 3
   \]

Thus, the value of \( T \) is **3**.

Let me know if you'd like more details or if you have any questions!

### Related Questions:
1. How would the value of \( T \) change if \( a - b = 2 \) and \( b - c = 2 \)?
2. What if the condition \( a - b = b - c = k \) was given with \( k = 4 \)?
3. How do different values of \( a - c \) impact the result?
4. Can we generalize the equation for \( T \) for any \( a - b = b - c \)?
5. What happens if the denominator in \( T \)'s equation changes?

**Tip:** When solving equations involving multiple variables, carefully handle each step to avoid calculation mistakes!

Si a - b = b - c = 3, calcula el valor de: T = ((a - b)^2 + (b - c)^2 + (a - c)^2) / 18

Calculate the value of T using algebraic concepts. This equation involves quadratic expressions and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation