The number of elements in the set {n Z : |n² - 10n + 19| 6} is

Question

The number of elements in the set ${n \in ℤ : | n^{2} - 10 n + 19 | < 6}$ is ________.

Smart Achievers · Accepted Answer

(6)

We have, $| n^{2} - 10 n + 19 |$ $< 6,$ $n \in ℤ$

$\Rightarrow$ $| {(n - 5)}^{2} - 6 |$ $< 6 \Rightarrow 0 < {(n - 5)}^{2} < 12$

$\Rightarrow$ ${(n - 5)}^{2} = 1, 4, 9 \Rightarrow n - 5 = \pm 1, \pm 2, \pm 3$

$∴$ $6 values of n exist.$

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