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Appropriate Question :- [for (ii) ]

x - 1/x = 2 then find x² - 1/x²

Formula Used :-

• (a - b)² = a² - 2ab + b²

Solution :-

Refer attachments for the answer

Extra Information :-

• (a - b)² = a² - 2ab + b²
• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a - b)³ = a³ - 3a²b + 3ab² - b³

Hope it helps you :)

Verified answer

EXPLANATION.

Question = 1.

⇒ (x² + 1/x²) = 5.

As we know that,

Formula of :

⇒ (a - b)² = a² + b² - 2ab.

Using this formula in this question, we get.

⇒ (x - 1/x)² = (x)² + (1/x)² - 2(x)(1/x).

⇒ (x - 1/x)² = x² + 1/x² - 2.

⇒ (x - 1/x)² = 5 - 2.

⇒ (x - 1/x)² = 3.

⇒ (x - 1/x) = ± √3.

∴ (x - 1/x) = ± √3.

Question = 2.

⇒ (x - 1/x) = 2.

As we know that,

Formula of :

⇒ (a - b)² = a² + b² - 2ab.

⇒ (a + b)² = a² + b² + 2ab.

⇒ (a² - b²) = (a - b)(a + b).

Using this formula in this question, we get.

Squaring on both sides of the equation, we get.

⇒ (x - 1/x)² = (2)².

⇒ (x)² + (1/x)² - 2(x)(1/x) = 4.

⇒ x² + 1/x² - 2 = 4.

⇒ x² + 1/x² = 4 + 2.

⇒ x² + 1/x² = 6.

⇒ (x + 1/x)² = (x)² + (1/x)² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

⇒ (x + 1/x)² = 6 + 2.

⇒ (x + 1/x)² = 8.

⇒ (x + 1/x) = ± √8.

⇒ (x + 1/x) = ± 2√2.

To find : (x² - 1/x²).

⇒ (x² - 1/x²) = (x - 1/x)(x + 1/x).

⇒ (x² - 1/x²) = (2)(± 2√2).

⇒ (x² - 1/x²) = ± 4√2.

∴ The value of (x² - 1/x²) = ± 4√2.