Question

if x + 1/x =4 ,find the values of

1) (x - 1/x )​

Answer 1

Values of x - 1/x is  ±2√3

Given:

x + 1/x  = 4

To Find:

Value of (x - 1/x)

Solution:

(a - b)² = (a + b)² - 4ab

Step 1:

Use the identity (a - b)² = (a + b)² - 4ab

a = x , b = 1/x

(x -1/x)² = (x + 1/x)² - 4x(1/x)

=> (x -1/x)² = (x + 1/x)² - 4

Step 2:

Substitute x + 1/x =4  and calculate value on RHS

(x -1/x)² = (4)² - 4

(x -1/x)² = 16 - 4

(x -1/x)² = 12

Step 3:

Taking square root on both sides

x - 1/x = ±√12

=> x - 1/x = ±2√3

values of x - 1/x is  ±2√3

Answer 2

Answer:

.,.,................