A binary operation x is defined by a x b = a\(^b\). If a x 2 = 2 - a, find the possible values of a?
A
1, -2
B
2, -1
C
2, -2
D
1, -1
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
a = b = a\(^2\)
a + 2 = a\(^2\).....(i)
a + 2 = 2 - a..............(ii)
a\(^2\) = 2 - a
a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0
= (a + 2)(a - 1) = 0
a = 1 or - 2
Source: Myschool Past Questions Archive (Record #56847)