Question

If x2 +1/x2=7 find the value of 2x2-2/2x2​

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Answer 1

your answer is in the attachment

Answer 2

Given :-

• (x² + 1/x²) = 7

To Find :-

• 2(x² - 1/x²) = ?

Solution :-

→ x² + 1/x² = 7

Adding 2 both sides we get,

→ x² + 1/x² + 2 = 7 + 2

→ x² + 1/x² + 2 * x * 1/x = 9

Comparing LHS, with a² + b² + 2ab = (a + b)² we get,

→ (x + 1/x)² = 9

Square root both sides we get,

→ (x + 1/x) = 3 ( Assuming Positive value only). ------- Equation (1)

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Now,

→ x² + 1/x² = 7

Subtracting 2 both sides we get,

→ x² + 1/x² - 2 = 7 - 2

→ x² + 1/x² - 2 * x * 1/x = 5

Comparing LHS, with a² + b² - 2ab = (a - b)² we get,

→ (x - 1/x)² = 5

Square root both sides we get,

→ (x - 1/x) = √5 ( Assuming Positive value only). ------- Equation (2)

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Now, we Have to Find :-

→ 2(x² - 1/x²)

Using (a² - b²) = (a+b)(a - b) we get,

→ 2(x + 1/x)(x - 1/x)

Putting Values Form Equation (1) & (2) Now, we get,

→ 2 * 3 * √5

→ 6√5 (Ans).

[ if we Take Negative Value Than also we will get same Answer ]..