Question

solve for x.
$(x - 2)^2 < 0$
write the solution using interval notation. use the union symbol ∪ to express the solution as a union of disjoint intervals. finite endpoints of all intervals should be integers. if there are no solutions, use the symbol ∅ for the empty set. use the set notation {a} to represent an isolated solution a.

Explanation:

Step1: Analyze the squared expression

A squared real number, $(x-2)^2$, is always non-negative, meaning $(x-2)^2 \geq 0$ for all real $x$.

Step2: Compare to the inequality

The inequality requires $(x-2)^2 < 0$, which contradicts the property of squared real numbers (no real number squared is negative).

Answer:

$\emptyset$