Mathematics

If (x + 5) is the geometric mean between (x + 2) and (x + 9), find the value of x.

2 Likes

Given, x + 5 is G.M. between x + 2 and x + 9.

$\therefore \dfrac{x + 2}{x + 5} = \dfrac{x + 5}{x + 9}$

⇒ (x + 5)² = (x + 2)(x + 9)

⇒ x² + 10x + 25 = x² + 9x + 2x + 18

⇒ x² + 10x + 25 = x² + 11x + 18

⇒ x² - x² + 10x - 11x = 18 - 25

⇒ -x = -7

⇒ x = 7.

Hence, the value of x = 7.

Answered By

1 Like