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Found problems: 2

2020 Vietnam National Olympiad, 2
Tags: inequation , inequalities , vmo , algebra
a)Let$a,b,c\in\mathbb{R}$ and $a^2+b^2+c^2=1$.Prove that: $|a-b|+|b-c|+|c-a|\le2\sqrt{2}$ b) Let $a_1,a_2,..a_{2019}\in\mathbb{R}$ and $\sum_{i=1}^{2019}a_i^2=1$.Find the maximum of: $S=|a_1-a_2|+|a_2-a_3|+...+|a_{2019}-a_1|$

2015 Bosnia And Herzegovina - Regional Olympiad, 1
Tags: algebra , inequation
Solve the inequation: $$5\mid x\mid \leq x(3x+2-2\sqrt{8-2x-x^2})$$