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I am a beginner at trying to prove or disprove inequalities. In an attempt to improve on this skill I found some problems that I would like to work on. Now, I know many of you may be able to look at this and think of a solution, but please refrain from posting it, but some advice and methods would be helpful.

Prove that in any acute triangle ABC with sides a, b, and c, the following inequality is true.

[tex] 27 \leq (a+b+c)^2 \left( \frac{1}{a^2 + b^2 - c^2}+\frac{1}{b^2 + c^2 - a^2}+\frac{1}{c^2 + a^2 - b^2} \right) [/tex]

Prove that in any acute triangle ABC with sides a, b, and c, the following inequality is true.

[tex] 27 \leq (a+b+c)^2 \left( \frac{1}{a^2 + b^2 - c^2}+\frac{1}{b^2 + c^2 - a^2}+\frac{1}{c^2 + a^2 - b^2} \right) [/tex]

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