INEQUALITY'S BLOG

December 8, 2011

Problem 309 van khea

Filed under: Problem by Van Khea — KKKVVV @ 6:48 am

If a, b, c are positive real numbers such that a+b+c=3. Prove that
\sqrt{1+a^4}+\sqrt{1+b^4}+\sqrt{1+c^4}\leq \sqrt{2}(a^2+b^2+c^2)

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December 5, 2011

Problem 307 vankhea

Filed under: Problem by Van Khea — KKKVVV @ 7:13 pm

if a, b, c are positive real numbers. Prove that:
\displaystyle (a^3+b^3)^2\geq \frac{1}{2}(a^4+b^4)(a+b)^2