Question

If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

When dealing with sums of squares, remember that each square must individually equal zero for the entire sum to be zero.

Answer 1

The Correct Option is A

Given the equation \( (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0 \), the sum of squares of three real numbers is zero only if each of the terms is zero. Hence: \[ a - 2 = 0, \quad b - 2 = 0, \quad c - 2 = 0 \] Thus, \(a = b = c = 2\), and therefore: \[ a + b + c = 2 + 2 + 2 = 6 \]