Answer:
We have the equation
[tex]a+x= 1+xa^2[/tex]
we leave the terms with x on the left side of the equation and the independent terms on the right side.
[tex]x-xa^2=1-a\\(1-a^2)x=1-a\\[/tex]
resolving for x we have that
[tex]x=\frac{1-a}{1-a^2}[/tex]
Since we need that the equation doesn't have solution, then it is necessary that the denominator of x be 0 and this occur when [tex]1-a^2=0\\1=a^2\\a=\pm1[/tex]
Then, for [tex]a=\pm1[/tex] the equation hasn't solution