Inegalitate OWN
Posted: Mon Dec 01, 2008 9:16 pm
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
\( a) \) \( \frac{1}{a+b-1}+\frac{1}{b+c-1}+\frac{1}{c+a-1} \geq \frac{9}{a^2+b^2+c^2 \)
\( b) \) \( \frac{a^2}{b+c-1}+\frac{b^}{c+a-1}+\frac{c^2}{a+b-1} \geq 3 \)
Claudiu Mindrila, R.M.T. 1/2009