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Omni-MATH / Let a,b,c be non-negative numbers with a+b+c=3. Prove the inequality

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problem

Let a,b,ca, b, c be non-negative numbers with a+b+c=3a+b+c = 3. Prove the inequality ab2+1+bc2+1+ca2+1≥32.\frac{a}{b^2+1}+\frac{b}{c^2+1}+\frac{c}{a^2+1} \geq \frac 32.
Plain-text mathematical notation (without MathML)
Let a,b,c be non-negative numbers with a+b+c=3. Prove the inequality
(a)/(b²+1)+(b)/(c²+1)+(c)/(a²+1)≥(3)/(2).
Original LaTeX notation
Let $a, b, c$ be non-negative numbers with $a+b+c = 3$. Prove the inequality
\[\frac{a}{b^2+1}+\frac{b}{c^2+1}+\frac{c}{a^2+1} \geq \frac 32.\]

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Source and history

task_id
1d0fe4f7-22b4-5c60-9bda-b72f72926f54
task_key
test--1d0fe4f7-22b4-5c60-9bda-b72f72926f54
task_revision_id
1
config / split
/ test

Official source

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