Question 126
If $a, b, c$ are real numbers such that two of them have difference greater than $\frac{1}{2\sqrt{2}}$, prove that there exists an integer $x$ such that
$$
x^2 - 4(a + b + c)x + 12(ab + bc + ca) \lt 0.
$$
$$
x^2 - 4(a + b + c)x + 12(ab + bc + ca) \lt 0.
$$