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Question
If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .
Options
233
33
55
-55
Solution
33
Given:- a * b = a2 − b2 + ab + 4
\[2 * 3 = 2^2 - 3^2 + 2 \times 3 + 4\]
\[ = 4 - 9 + 6 + 4\]
\[ = 5\]
\[\left( 2 * 3 \right) * 4 = 5 * 4\]
\[ = 5^2 - 4^2 + 5 \times 4 + 4\]
\[ = 25 - 16 + 20 + 4\]
\[ = 33\]
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