Word Count : 304

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To prove the inequality: \[ \frac{1}{2}(x + y + z) \leq \frac{x^2}{y + z} + \frac{y^2}{x + z} + \frac{z^2}{x + y}, \quad \text{for } x, y, z > 0, \] we will use the Cauchy-Schwarz Inequality in the form of Titu's Lemma, which states that for positive real numbers \(a_1, a_2, \dots, a_n\) and \(b_1, b_2, \dots, b_n\), \[ ___ ___ _____ ____ ______ _____ ____ __________ _____ ____.
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