turkey-yks 2024 Q5

turkey-yks · Other · yks-ayt Inequalities Integer Solutions of an Inequality
Let $a$ be an integer. There are exactly 4 integer values of $x$ satisfying
$$0 < \left| x^{2} - 2x + 2 \right| - x^{2} - x < a$$
What is the sum of the different integer values that $a$ can take?
A) 33 B) 36 C) 39 D) 42 E) 45
Let $a$ be an integer. There are exactly 4 integer values of $x$ satisfying

$$0 < \left| x^{2} - 2x + 2 \right| - x^{2} - x < a$$

What is the sum of the different integer values that $a$ can take?

A) 33
B) 36
C) 39
D) 42
E) 45