a) Cho a_1 \leq a_2,b_1 \leq b_2. Chứng minh \dfrac{a_1b_1+a_2b_2}{2} \geq \dfrac{a_1+a_2}{2}.\dfrac{b_1+b_2}{2}
b) Cho a_1 \leq a_2,b_1 \geq b_2. Chứng minh \dfrac{a_1b_1+a_2b_2}{2} \leq \dfrac{a_1+a_2}{2}.\dfrac{b_1+b_2}{2}
c) Cho x,y \geq 0. Chứng minh \dfrac{x^{100}+y^{100}}{2} \geq...