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  • The number of elements in the set  <img alt="\left\{n \in Z:\left|n^2-10 n+19\right|<6\right\}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%5C%7Bn%20%5Cin%20Z%3A%5Clef

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

Option: 1

6


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

$$ \begin{aligned} & -6<n^2-10 n+19<6 \\ & \Rightarrow \mathrm{n}^2-10 n+25>0 \text { and } \\ & (n-5)^2>0 \\ & N \in Z-\{5\} \end{aligned}.....(i)                             \begin{aligned} & \mathrm{n}^2-10 \mathrm{n}+13<0 \\ & 5-3 \sqrt{2}<\mathrm{n}<5+3 \sqrt{2} \\ & \mathrm{n}=\{2,3,4,5,6,7,8\} \end{aligned}    .....(ii)

From (i) \cap (ii)
N = {2, 3, 4, 5, 6, 8,}
Number of values of n = 6

Posted by

seema garhwal

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