Question

pls anser this question

Answer 1

Let (x - 1/x) = p

Cubing on both sides of the equation,

(x - 1/x)3 = p3

x3 - 1/x3 - 3(x - 1/x) = p3

(14) - 3p = p3 [Given that x3 - 1/x3 = 14]

p3 + 3p - 14 = 0

(p - 2) is a factor of (p3 + 3p - 14) as p(2) = 0. [According to remainder theorem]

Therefore the other factor of (p3 + 3p - 14) on dividing by (p - 2) is (p2 + 2p + 7).

⇒ (p - 2)(p2 + 2p + 7) = 0

⇒ p = 2

The other values of p are not real numbers as (p2 + 2p + 7) can not be factored.

Therefore, (x - 1/x) = 2.