Question

If (x+1/x)=6


Find 1. (x-1/x)

2. (x²-1/x²)

Answer 1

$\huge\boxed {Answer}$

Given :-

x + 1/x = 6

To Find out :-

(x - 1/x) & (x² - 1/x²)

Explanation :-

Here , x + 1/x = 6 -----(1)

Doing square both side

x² + 1/x² + 2 = 36

x² + 1/x² = 34

x² + 1/x² - 2 = 32

(x - 1/x)² = 32

x - 1/x = 4√2 ------(2)

Now , eq.(1) × eq.(2)

(x + 1/x) (x - 1/x) = 6 × 4√2

x² - 1/x² = 24√2

Result :-

(1) (x - 1/x) = 4√2

(2) (x² - 1/x²) = 24√2