Inegalitate 5
Posted: Wed Feb 04, 2009 10:54 pm
Daca a,b,c sunt pozitive atunci
\( \frac{(a+b)^2}{c}+\frac{c^2}{a}\ge 4b \)
T. Andreescu M.R.
\( \frac{(a+b)^2}{c}+\frac{c^2}{a}\ge 4b \)
T. Andreescu M.R.
Din Titu Andreescu avem ca :
\( LHS\ge \frac{(a+b+c)^2}{c+a} \) si e suficient sa aratam ca \( \frac{(a+b+c)^2}{c+a}\ge 4b \Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca\ge 4ab+4bc \Leftrightarrow (a-b+c)^2\ge 0 \)