Question

product : (x-1/x) (x+1/x) (x²+1/x²)​

Answer 1

Answer :-

$\tt x^4 - \dfrac{1}{x^4}$

Solution :-

(x - 1/x)(x + 1/x)(x² + 1/x²)

= {(x)² - (1/x)²}(x² + 1/x²)

[Because (a + b)(a - b) = a² - b² and above a = x and b = 1/x]

= (x² - 1²/x²)(x² + 1/x²)

= (x² - 1/x²)(x² + 1/x²)

= (x²)² - (1/x²)²

[Because (a + b)(a - b) = a² - b² and above a = x² and b = 1/x²]

$\sf = x^{2*2} - \dfrac{(1)^2}{(x^2)^2}$

$\sf = x^4 - \dfrac{1}{x^{2*2}}$

$\bf = x^4 - \dfrac{1}{x^4}$

Identity used :-

• (a + b)(a - b)

Answer 2

Answer:

Answer :-

\tt x^4 - \dfrac{1}{x^4}x

4

−

x

4

1

Solution :-

(x - 1/x)(x + 1/x)(x² + 1/x²)

= {(x)² - (1/x)²}(x² + 1/x²)

[Because (a + b)(a - b) = a² - b² and above a = x and b = 1/x]

= (x² - 1²/x²)(x² + 1/x²)

= (x² - 1/x²)(x² + 1/x²)

= (x²)² - (1/x²)²

[Because (a + b)(a - b) = a² - b² and above a = x² and b = 1/x²]

\sf = x^{2*2} - \dfrac{(1)^2}{(x^2)^2}=x

2∗2

−

(x

2

)

2

(1)

2

\sf = x^4 - \dfrac{1}{x^{2*2}}=x

4

−

x

2∗2

1

\bf = x^4 - \dfrac{1}{x^4}=x

4

−

x

4

1

Identity used :-

(a + b)(a - b)