Mathematics, 21.06.2021 14:00 andrew763
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Find the smallest positive value of the nonnegative number \lambdaλ such that the inequality
\frac{a+b}{2}\ge \lambda \sqrt{ab}+(1-\lambda) \sqrt{\frac{a^2+b^2}{2}}
2
a+b
≥λ
ab
+(1−λ)
2
a
2
+b
2
holds for all positive real numbers a, ba, b.
Answers: 1
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