The number of elements in the set left{n in Z | vedclass

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Question

$-6 < n ^2-10 n +19 < 6$ $\Rightarrow n^2-10 n+25 > 0 ext { and } n ^2-10 n +13 < ( n -5)^2 > 0 n \in[5-2 \sqrt{3}, 5+2 \sqrt{3}]$

Vedclass · Accepted Answer

$6$

Vedclass · Answer

$-6 < n ^2-10 n +19 < 6$ $\Rightarrow n^2-10 n+25 > 0 ext { and } n ^2-10 n +13 < ( n -5)^2 > 0 n \in[5-2 \sqrt{3}, 5+2 \sqrt{3}]$ $n \in R-[5]$ $ herefore n \in[1.3,8.3]$ $\Rightarrow n=2,3,4,6,7,8$

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

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