Correct option is C
Given:
1. a, b, c are three consecutive integers.
2. Their sum is 15: a + b + c = 15.
3. We need to calculate (a - 2)² + (b - 2)² + (c - 2)².
Concept:
Consecutive integers can be written as a = x - 1, b = x, c = x + 1, where x is the middle integer. The sum of the integers is (x - 1) + x + (x + 1) = 3x.
Solution:
Step 1: Solve for x
Since a + b + c = 15, 3x = 15, x = 5.
Thus, the integers are: a = 4, b = 5, c = 6.
Step 2: Calculate (a - 2)² + (b - 2)² + (c - 2)²
1. (a - 2)² = (4 - 2)² = 2² = 4.
2. (b - 2)² = (5 - 2)² = 3² = 9.
3. (c - 2)² = (6 - 2)² = 4² = 16.
Adding these: (a - 2)² + (b - 2)² + (c - 2)² = 4 + 9 + 16 = 29.
Conclusion:
The value is 29.
Answer: (c). 29
