Demonstrati ca pentru orice \( a,b,c\in\left(\frac{1}{2},+\infty\right) \) au loc inegalitatile:
\( a) \) \( \frac{1}{a+b-1}+\frac{1}{b+c-1}+\frac{1}{c+a-1} \geq \frac{9}{a^2+b^2+c^2 \)
\( b) \) \( \frac{a^2}{b+c-1}+\frac{b^}{c+a-1}+\frac{c^2}{a+b-1} \geq 3 \)
Claudiu Mindrila, R.M.T. 1/2009
Inegalitate OWN
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Claudiu Mindrila
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Inegalitate OWN
Last edited by Claudiu Mindrila on Tue Feb 17, 2009 11:02 pm, edited 1 time in total.
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