Given are six reals $a, b, c, x, y, z$ such that $(a + b + c)(x + y + z) = 3$ and $(a^2 + b^2 + c^2)(x^2 + y^2 + z^2) = 4$. Prove that $ax + by + cz \ge 0$.
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Tags: inequalities, 2nd edition
Given are six reals $a, b, c, x, y, z$ such that $(a + b + c)(x + y + z) = 3$ and $(a^2 + b^2 + c^2)(x^2 + y^2 + z^2) = 4$. Prove that $ax + by + cz \ge 0$.