23.03.2012 - inegalitati [cls VII-VIII]
Scris: Joi Mar 22, 2012 3:30 pm
Fie $a,b,c,x,y,z \in \mathbb {R}$ si $A = ax + by + cz,\ B = ay + bz + cx,\ C = az + bx + cy$.
Daca ${\left| {A - B} \right|} \ge 1,\ {\left| {B - C} \right|} \ge 1$ si ${\left| {C - A} \right|} \ge 1$, aratati ca $\left( a^{2} + b^{2} + c^{2}} \right)\left( {x^{2} + y^{2} + z^{2}} \right) \geq \frac{4}{3}$.
sursa: Adrian Zahariuc
Daca ${\left| {A - B} \right|} \ge 1,\ {\left| {B - C} \right|} \ge 1$ si ${\left| {C - A} \right|} \ge 1$, aratati ca $\left( a^{2} + b^{2} + c^{2}} \right)\left( {x^{2} + y^{2} + z^{2}} \right) \geq \frac{4}{3}$.
sursa: Adrian Zahariuc