JAMB 2000 · UME · Q12

A binary operation $*$ is defined by $a * b = a^b$ . If $a * 2 = 2 - a$ , find the possible values of $a$ .

Worked solution (try it first)

$a * 2 = a^2$ , so the equation is $a^2 = 2 - a$ .
Bring everything to one side: $a^2 + a - 2 = 0$ , which factorises as $(a - 1)(a + 2) = 0$ .
So $a = 1$ or $a = -2$ , option D.