Sets, Relations & Functions
Count of Integer Solutions of Absolute Value Inequality
nta_pyq_2023_apr
Grade 11
Question:
The number of elements in $\{n\in\mathbb{Z}:\ |n^2-10n+19|<6\}$ is _______.
Step-by-Step Solution
Key Concept: $|n^2-10n+19|<6\Rightarrow-6<n^2-10n+19<6$. First: $(n-5)^2>0$ (all $n\neq5$). Second: $n^2-10n+13<0\Rightarrow n\in(5-2\sqrt{3},5+2\sqrt{3})\approx(1.54,8.46)$.
6 elements.
Correct Answer: 6