[tex] \it x\circ y = 4(x+y-3) -xy = 4x+4y-12-xy = 4x+4y-16+4-xy =
\\ \\
= (4x-16) - (xy-4y) +4 = 4(x-4) -y(x-4) +4 =
\\ \\
= (x-4)(4-y) +4 = -(x-4)(y-4) +4 = 4-(x-4)(y-4) [/tex]
[tex] \it x\circ x = 4- (x-4)^2
\\ \\
x\circ x \circ x = [4- (x-4)^2] \circ x = 4-(4- (x-4)^2-4)(x-4) =
\\ \\
= 4+(x-4)^2(x-4) [/tex]
[tex] \it x\circ x\circ x = x \Rightarrow 4+(x-4)^2(x-4) =x \Rightarrow
\\ \\
\Rightarrow -x + 4+(x-4)^2(x-4) = 0 \Rightarrow -(x-4) 4+(x-4)^2(x-4) =0
\\ \\
\Rightarrow (x-4)[(x-4)^2 -1]=0 \Rightarrow (x-4)(x-4-1)(x-4+1) =0 \Rightarrow
\\ \\
\Rightarrow (x-4)(x-5)(x-3) = 0 \Rightarrow x \in \{3,\ 4,\ 5\} [/tex]
