OlympiadHardInequalities10–12

Cauchy-Schwarz Inequality

Desigualdade de Cauchy-Schwarz

For positive reals $a, b, c$ , prove that: $(a^{2} + b^{2} + c^{2})\left(\tfrac{1}{a^{2}} + \tfrac{1}{b^{2}} + \tfrac{1}{c^{2}}\right) \ge 9$

Apply the Cauchy-Schwarz inequality in its standard form to $(a, b, c)$ and $\left(\tfrac{1}{a}, \tfrac{1}{b}, \tfrac{1}{c}\right)$ .

Solution

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