A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a.
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Correct Answer: Option D
Explanation:
a * b = a\(^b\)
a * 2 = a\(^2\) = 2 - a
a\(^2\) + a - 2 = 0
a\(^2\) + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2
a * b = a\(^b\)
a * 2 = a\(^2\) = 2 - a
a\(^2\) + a - 2 = 0
a\(^2\) + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2