Find the value of $a^4-a^3+a^2+2$ when $a^2+2=2a$ Find the value of $a^4-a^3+a^2+2$ when $a^2+2=2a$
My Attempt, 
$$a^4-a^3+a^2+2=a^4-a^3+2a$$
$$=a(a^3-a^2+2)$$
What's next?

Obviously $a \not = 0$. Then we have $a^4 = 2a^3 - 2a^2$ by multiplying the condition by $a^2$, so the equation becomes: $a^3 - a^2 + 2$. Similarly $a^3 = 2a^2 - 2a$, so the equation becomes: $a^2 - 2a + 2 = 0$
