Question

23. Solve this question
Please give verified answer with step by step solution​

Answer 1

Answer: x⁸ - 1/x⁸

Step by step explanation:

We'll use the identity: (a + b) (a - b) = a²- b².

Given: [x - 1/x] [x + 1/x] [x² + 1/x²] [x⁴ + 1/x⁴]

= [x² - 1/x²][x² + 1/x²][x⁴ + 1/x⁴]

= [(x²)² - (1/x²)²] [x⁴ + 1/x⁴]

= [x⁴- 1/x⁴] [x + 1/x⁴]

= (x⁴)² - (1/x⁴)²

= x⁸-1/x⁸

Thus, the answer is x⁸-1/x⁸.

Answer 2

Answer

We need to find the product

$\rm (x - \frac { 1 } { x }) × (x + \frac { 1 } { x }) × (x^2 + \frac { 1 } { x^2 }) × (x^4 + \frac { 1 } { x^4 } )$

We know that :

(a + b)(a - b) = a² - b²

So,

⇛ $\rm (x^2 - (\frac { 1 } { x })^2) × (x^2 + \frac { 1 } { x^2 }) × (x^4 + \frac { 1 } { x^4 } )$

We know that :

(a + b)(a - b) = a² - b²

⇛ $\rm (x^4 - (\frac { 1 } { x } )^4 ) × (x^4 + \frac { 1 } { x^4 } )$

We know that :

(a + b)(a - b) = a² - b²

⇛ $\rm x^{16} - (\frac { 1 } { x } )^{16}$

i.e

⇛ $\rm x^{16} - \frac { 1 } { x^{16}}$