a = 1+a^2. Since a can't equal zero, (then 0 = 1), I can divide by a, yielding

1=1/a + a. Substituting for 1 in the original equation,

a=1/a + a + a^2

-1/a = a^2

-1=a^3

a=-1

Checking into the original equation,

-1 = 1+(-1)^2

-1=2

Clearly, -1 doesn't equal two- however, can you find the error?