Let a≥b≥c≥d>0 and a+b+c+d = 4. Prove that (((√a)+(√b)+(√c))/3) ≤ (1/( (√d))) Prove if ∀n∈N^+ , then (((a)^(1/n) +(b)^(1/n) +(c)^(1/n) )/3) ≤ (1/( (d)^(1/n) ))


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Question Number 142914 by loveineq last updated on 07/Jun/21

$Let a ⩾ b ⩾ c ⩾ d > 0 and a + b + c + d = 4 .$ $Prove that$ $\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{3} ⩽ \frac{1}{\sqrt{d}}$ $Prove if \forall n \in N^{+}, then$ $\frac{\sqrt[n]{a} + \sqrt[n]{b} + \sqrt[n]{c}}{3} ⩽ \frac{1}{\sqrt[n]{d}}$
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