Word Count : 373

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सिद्ध करने के लिए हम इस असमानता को: \[ \frac{1}{2}(x + y + z) \le \frac{x^2}{y + z} + \frac{y^2}{x + z} + \frac{z^2}{x + y} \] हमें साबित करना है कि यह असमानता \( x, y, z > 0 \) के लिए सही है। इसे हम Cauchy-Schwarz inequality का उपयोग करके सिद्ध करेंगे। ### Cauchy-Schwarz Inequality का रूप: Cauchy-Schwarz inequality कहती है कि: \[ \left( \sum_{i=1}^{n} a_i b_i \right)^2 \le \left( \sum_{i=1}^{n} a_i^2 \right) \left( \sum_{i=1}^{n} b_i^2 \right) \] हमारे मामले में, हम इसे लागू करेंगे। पहले, असमानता को इस रूप में ___ _________ ____ ______ ______ __________ ____.
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