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Omni-MATH / Let a,b,c,d be non-negative reals such that a+b+c+d=4. Prove the inequality

Problem

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problem

Let a,b,c,da,b,c,d be non-negative reals such that a+b+c+d=4a+b+c+d=4. Prove the inequality aa3+8+bb3+8+cc3+8+dd3+8≤49\frac{a}{a^3+8}+\frac{b}{b^3+8}+\frac{c}{c^3+8}+\frac{d}{d^3+8}\le\frac{4}{9}
Plain-text mathematical notation (without MathML)
Let a,b,c,d be non-negative reals such that a+b+c+d=4. Prove the inequality
(a)/(a³+8)+(b)/(b³+8)+(c)/(c³+8)+(d)/(d³+8)≤(4)/(9)
Original LaTeX notation
Let $a,b,c,d$ be non-negative reals such that $a+b+c+d=4$. Prove the inequality
\[\frac{a}{a^3+8}+\frac{b}{b^3+8}+\frac{c}{c^3+8}+\frac{d}{d^3+8}\le\frac{4}{9}\]

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Source and history

task_id
ce2cdcde-1054-509d-b355-a66e84252675
task_key
test--ce2cdcde-1054-509d-b355-a66e84252675
task_revision_id
1
config / split
/ test

Official source

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