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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
Solution
445
Given: a * b = a2 + b2 + ab + 1
\[2 * 3 = 2^2 + 3^2 + 2 \times 3 + 1\]
\[ = 4 + 9 + 6 + 1\]
\[ = 20\]
\[\left( 2 * 3 \right) * 2 = 20 * 2\]
\[ = {20}^2 + 2^2 + 20 \times 2 + 1\]
\[ = 400 + 4 + 40 + 1\]
\[ = 445\]
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