For x > 0, if the arithmetic mean of x² and 1/x² is M², then mean of x and 1/x is
The square of the mean of x and 1/x is (x² + 2 + 1/x²)/4. Since x² + 1/x² = 2M², this equals (2M² + 2)/4 = (M² + 1)/2. For positive x the mean is positive, so it equals…
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For x > 0, if the arithmetic mean of x² and 1/x² is M², then mean of x and 1/x is
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Correct answer C
The square of the mean of x and 1/x is (x² + 2 + 1/x²)/4. Since x² + 1/x² = 2M², this equals (2M² + 2)/4 = (M² + 1)/2. For positive x the mean is positive, so it equals √((M² + 1)/2).
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