Question 159
Let $P(x)$, $Q(x)$ and $R(x)$ be polynomials, such that $Q(x)$ and $R(x)$ take nonnegative values only. It is known, that the equation
$$
P(x) + \sqrt{Q(x)} + \sqrt{Q(x) + \sqrt{R(x)}} = 0
$$
has infinitely many solutions. Is it true, that every real number is a root of this equation?
$$
P(x) + \sqrt{Q(x)} + \sqrt{Q(x) + \sqrt{R(x)}} = 0
$$
has infinitely many solutions. Is it true, that every real number is a root of this equation?