# math contest – I do not know where to use the hypothesis

Let a real number such as $$| a | > 2$$. Prove that if $$a ^ {4} -4a ^ {2} + 2$$ and $$a ^ 5-5a ^ 3 + 5a$$ are rational numbers, so $$a$$ is a rational number too.

My attempt is the following.
$$a ^ 5-5a ^ 3 + 5a = a (a ^ {4} -4a ^ {2} +2-a ^ 2 + 3)$$. Who can be written as $$a ( frac {c} {d} -a ^ 2 + 3)$$ for some people $$c, d$$ in the integers. Note, $$a ( frac {c} {d} -a ^ 2 + 3) = frac {g} {h}$$ by our hypothesis. Now we have $$frac {ac-da ^ 3 + 3ad} {d} = frac {g} {h}$$. I played with the expression but I can not seem to get the result.