Question

X=}" align="absmiddle" class="latex-formula"> x ∈ N, n ∈ N

Answer 1

Answer:

x = {3,4,7,12}

n = {12,7,4,3}

(upside down)

Step-by-step explanation:

N = {1,2,3,4,5....}

$\:$

if n = 1

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(1) + 6}{1 - 2}}$

$\sf{x = \frac{2 + 6}{-1}}$

$\sf{x = \frac{8}{-1}}$

$\sf{x = - 8}$

• x not N

$\:$

if n = 2

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(2) +6}{2-2}}$

$\sf{x = \frac{4 + 6}{2 - 2}}$

$\sf{x = \frac{8}{0}}$

$\sf{x = \infty }$

• x not N

$\:$

if n = 3

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(3) +6}{3-2}}$

$\sf{x = \frac{6 + 6}{1}}$

$\sf{x = \frac{12}{1}}$

$\sf{x = 12}$

• x is N

$\:$

if n = 4

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(4) +6}{4-2}}$

$\sf{x = \frac{8 + 6}{2}}$

$\sf{x = \frac{14}{2}}$

$\sf{x = 7}$

• x is N

$\:$

if n = 5

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(5) +6}{5-2}}$

$\sf{x = \frac{10 + 6}{3}}$

$\sf{x = \frac{16}{3}}$

• x not N

$\:$

if n = 6

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(6) +6}{6-2}}$

$\sf{x = \frac{12 + 6}{4}}$

$\sf{x = \frac{18}{4}}$

• x not N

$\:$

if n = 7

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(7) +6}{7-2}}$

$\sf{x = \frac{14 + 6}{5}}$

$\sf{x = \frac{20}{5}}$

$\sf{x = 4}$

• x is N

$\:$

if n = 12

$\sf{x = \frac{2n+6}{n-2}}$

$\sf{x = \frac{2(12) +6}{12-2}}$

$\sf{x = \frac{24 + 6}{10}}$

$\sf{x = \frac{30}{10}}$

$\sf{x = 3}$

• x is N

$\:$

conclusion

• I found the pattern of numbers that the value of n is 3, 4, 7,12
• For x, I found the pattern of numbers that the value of x is 12, 7, 4,3