Monic poly

Let P(x) and Q(x) be (monic) polynomials with real coe fficients (the fi rst coeffi cient being equal to 1), and
deg P(x) = deg Q(x) = 10. Prove that if the equation P(x) = Q(x) has no real solutions, 
then P(x + 1) = Q(x - 1) has a real solution.