Home Competitions AUSTRIAN-POLISH 1993 Problem 6
AUSTRIAN-POLISH 1993 Problem 6
If a , b ≥ 0 a,b \ge 0 a , b ≥ 0 ( a + b 2 ) 2 ≤ a + a 2 b 3 + a b 2 3 + b 4 ≤ a + a b + b 3 ≤ ( a 2 / 3 + b 2 / 3 2 ) 3 \left(\frac{\sqrt{a}+\sqrt{b}}{2}\right)^2\leq\frac{a+\sqrt[3] {a^2b}+\sqrt[3] {ab^2}+b}{4}\leq\frac{a+\sqrt{ab}+b}{3} \leq \sqrt{\left(\frac{a^{2/3}+b^{2/3}}{2}\right)^{3}} ( 2 a + b ) 2 ≤ 4 a + 3 a 2 b + 3 a b 2 + b ≤ 3 a + ab + b ≤ ( 2 a 2/3 + b 2/3 ) 3
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