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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