Question

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Answer 1

Step-by-step explanation:

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Answer 2

Question :-

If x + 1/x = p, then value of x - 1/x is :

(a) p² - 4

(b) p² + 4

(c) √( p² + 4 )

(d) √( p² - 4 )

Answer :-

(d) √( p² - 4 )

Explanation :-

x + 1/x = p

Squaring on both sides

⇒ (x + 1/x)² = p²

⇒ (x)² + (1/x)² + 2(x)(1/x) = p²

[ Because (a + b)² = a² + b² + 2ab ]

⇒ x² + (1/x)² + 2 = p²

⇒ x² + (1/x)² = p² - 2

Subtracting 2 on both sides

⇒ x² + (1/x)² - 2 = p² - 2 - 2

⇒ x² + (1/x)² - 2(x)(1/x) = p² - 4

[ Because (a - b)² = a² + b² - 2ab ]

⇒ (x - 1/x)² = p² - 4

Taking square root on both sides

⇒ x - 1/x = √( p² - 4 )

Another way

We know that

(a - b)² = (a + b)² - 4ab

Here

• a = x

• b = 1/x

By substituting the values

⇒ (x - 1/x)² = (x + 1/x)² - 4(x)(1/x)

⇒ (x - 1/x)² = p² - 4

[ Because x + 1/x = p ]

Taking square root on both sides

⇒ x - 1/x = √( p² - 4 )