Question

If x + 1/x = 5 and x - 1/x = 3, then x^2 - 1/x^2 = ?

Answer 1

Answer:

the answer of this Q is ⁸⁹

Answer 2

Answer:-

Given:

x + 1/x = 5 -- equation (1)

x - 1/x = 3 -- equation (2).

On Multiplying equation (1) & (2) we get,

→ (x + 1/x) * (x - 1/x) = 5 * 3

We know that,

a² - b² = (a + b)(a - b)

Let,

• a = x
• b = 1/x

Hence,

(x)² - (1/x)² = 15

→ x² - 1/x² = 15

(or)

Adding equations (1) & (2) we get,

x + 1/x + x - 1/x = 5 + 3

→ 2x = 8

→ x = 8/2

→ x = 4

Putting the value of x in equation (1) we get,

→ 4 + 1/x = 5

→ 1/x = 5 - 4

→ 1/x = 1

Hence,

→ x² - 1/x² = (4)² - (1)²

→ x² - 1/x² = 16 - 1

→ x² - 1/x² = 15

Hence, the value of x² - 1/x² is 15.