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Thought inequality

Say and prove for what values of \(\epsilon\) is true, for any pair of real positive numbers \(a, b\) the following inequality: \(\epsilon\sqrt{ab} + (1 - \epsilon)\sqrt{\frac{a^{2}+ b^{2}}{2}}\) \(\le \frac{a+b}{2}\)

Note by Jordi Bosch
3 years ago

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