A binary operation * is defined by a * b = a(^b). If a * 2 = 2 – a, find the possible values of a.
-
A.
1, -1 -
B.
1, 2 -
C.
2, -2 -
D.
1, -2
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