Question:medium

Let \( A \) and \( G \) denote the arithmetic mean and geometric mean of positive real numbers \( 5^x \) and \( 5^{1 - x} \). Then the minimum value of the expression \[ 5^x + 5^{1 - x}, \text{ where } x \in \mathbb{R}, \text{ is:} \]

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The AM-GM inequality states that the arithmetic mean is always greater than or equal to the geometric mean, and equality holds when all the terms are equal.
Updated On: May 5, 2026
  • \( 2\sqrt{5} \)
  • 0
  • 1
  • \( \sqrt{5} \)
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The Correct Option is A

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