Word Count : 207

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We are given the inequality to prove: $$ \frac{1}{2}(x + y + z) \leq \frac{x^2}{y+z} + \frac{y^2}{x+z} + \frac{z^2}{x+y} \quad \text{for } x, y, z > 0 $$ --- ### Approach: Use Titu’s Lemma (a.k.a. Engel’s Inequality) Titu’s Lemma states: > For positive real numbers $a_1, a_2, \dots, a_n$ and $b_1, __________ ___ __________ ________ _____ ___ ___ __________ _________ ____.
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