Question

If operation 'o' is defined as \( (a \, o \, b) = a^2 + b^2 - ab \), then \( (1 \, o \, 2) \, o \, 3 \) is?

• A. 18
• B. 27
• C. 9
• D. 12

Hint:

When solving for composite operations, always work step-by-step and carefully apply the operation definition to each step.

Answer 1

The Correct Option is B

We are given the operation \( (a \, o \, b) = a^2 + b^2 - ab \). First, calculate \( 1 \, o \, 2 \): \[ 1 \, o \, 2 = 1^2 + 2^2 - 1 \times 2 = 1 + 4 - 2 = 3 \] Next, calculate \( 3 \, o \, 3 \) using the same operation: \[ 3 \, o \, 3 = 3^2 + 3^2 - 3 \times 3 = 9 + 9 - 9 = 9 \] So, \( (1 \, o \, 2) \, o \, 3 = 9 \). Thus, the correct answer is 9. So, the answer is (C) 9. There was a misunderstanding in the previous evaluation.