Question

please solve it fast​

Answer 1

Answer:

7 is the best answer for this question

Step-by-step explanation:

please Mark me brainliestest answer

Answer 2

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : |m - n| \\ \\ given \: that \\ 2,m,n \: are \: in \: AP \\ m,n,9 \: are \: in \: GP \\ \\ thus \: then \\ m - 2 = n - m \\ 2m = n + 2 \\ \\ m = \frac{n + 2}{2} \: \: \: \: \: \: (1) \\ \\ \frac{n}{m} = \frac{9}{n} \\ \\ n {}^{2} = 9m \: \: \\ \\ n {}^{2} = 9( \frac{n + 2}{2} ) \\ \\ 2n {}^{2} = 9(n + 2) \\ \\ 2n {}^{2} - 9n - 18 = 0 \\ \\ 2n {}^{2} - 12n + 3n - 18 = 0 \\ \\ (2n + 3)(n - 6) = 0 \\ \\ n = - \frac{3}{2} \: \: or \: \: n = 6 \\ \\ but \: as \: m,n∈N \\ n = - \frac{3}{2} \: \: is \: absurd \\ \\ n = 6 \\ \\ so \: from \: (1) \\ we \: get \\ m = 4 \\ \\ thus \: s o\\ |m - n| = |4 - 6| = | - 2| = 2 \\ \\ therefore \: \\ |m - n| = 2$