2.5 Inequalities

Let \(a, b, c\) be positive real numbers. Prove that: i) \(a^2 + b^2 + c^2 \ge ab + bc + ca\) ii) \(a^3 + b^3 + c^3 + ab^2 + bc^2 + ca^2 \ge 2(a^2b + b^2c + c^2a)\)

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