Question

1/x-1/x-2=3 where x cannot be equal to 0 find x

Answer 1

Solution for x: x = 1 ± 1/3 * √3

Explanation:

∴ 1/x - 1/(x - 2) = 3

⇒ (x - 2 - x) / {x (x - 2)} = 3

⇒ - 2 = 3 x (x - 2)

⇒ - 2 = 3x² - 6x

⇒ 3x² - 6x + 2 = 0

Using Sridhar Acharya'a rule, we get

x = [- (- 6) ± √{(- 6)² - 4 * 3 * 2}] / (2 * 3)

= {6 ± √(36 - 24)}/6

= (6 ± √12)/6

= {6 ± 2√3}/6

= 1 ± 1/3 * √3