Question

The binary operation * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is equal to ______________ .

Options

• 20

• 40

• 400

• 445

Answer 1

445
Given: a * b = a² + b² + ab + 1

\[2 * 3 = 2^2 + 3^2 + 2 \times 3 + 1\]
        \[ = 4 + 9 + 6 + 1\]
        \[ = 20\]
\[\left( 2 * 3 \right) * 2 = 20 * 2\]
       \[ = {20}^2 + 2^2 + 20 \times 2 + 1\]
       \[ = 400 + 4 + 40 + 1\]
       \[ = 445\]