If the average of x and \(\frac{1}{x}\) (x ≠ 0) is m, then the average of x² and \(\rm \frac{1}{x^2}\) is:

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UP Police Constable Re-Exam 2024 Official Paper (Held On: 23 Aug, 2024 Shift 1)

Answer 1

Given:

Average of x and 1/x = m

Formula used:

Average of a and b = (a + b)/2

Calculation:

m = (x + 1/x)/2

⇒ x + 1/x = 2m

Now, average of x² and 1/x² = (x² + 1/x²)/2

x² + 1/x² = (x + 1/x)² - 2

⇒ x² + 1/x² = (2m)² - 2

⇒ Average of x² and 1/x² = [(2m)² - 2]/2

⇒ = 2m² - 1

∴ The correct answer is option (1).

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