Cho a \(\ge\) 0, b \(\ge\) 0, c \(\ge\) 0. Chứng minh rằng:
a) \(\dfrac{a+b}{2}\) \(\ge\) \(\sqrt{ab}\) (bất đẳng thức Cô-si) ;
b) a + b + c \(\ge\) \(\sqrt{ab}\) + \(\sqrt{bc}\) + \(\sqrt{ca}\) ;
c) a + b + \(\dfrac{1}{2}\) \(\ge\) \(\sqrt{a}\) + \(\sqrt{b}\) ;