Question

If X = 1/X-2√3, Find The Values Of

(1) X-1/X
(2) X+1/X​

Answer 1

Answer:-

Given:

x = 1/(x - 2√3)

⟶ x(x - 2√3) = 1

⟶ x - 2√3 = 1/x

⟶ - 2√3 = 1/x - x

Multiply ( - 1) on both sides.

⟶ 2√3 = x - 1/x

⟶ x - 1/x = 2√3

We know that,

(a + b)² - (a - b)² = 4ab

So,

⟶ (x + 1/x)² - (x - 1/x)² = 4 * x * 1/x

⟶ (x + 1/x)² - (2√3)² = 4

⟶ (x + 1/x)² = 4 + 12

⟶ (x + 1/x)² = 16

⟶ (x + 1/x) = √16

⟶ x + 1/x = ± 4

∴

• x - 1/x = 2√3
• x + 1/x = ± 4.