Integers That Allow a Solution

★ 5/10Extrema Absolute Value algebra inequality Casework

Problem

Suppose there exists $x \in \mathbb{R}$ such that

x^2 + |x - a| - 2 < 0,

where $a \in \mathbb{Z}$ . Find the sum of all integers $a$ satisfying this condition.

Answer

Solution

Difficulty	5/10
Topics	Extrema, Absolute Value, algebra, inequality, Casework

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