a) có: \((a-b)^2 \ge0\)
\(\Leftrightarrow a^2-2ab+b^2 \ge0\)
\(\Leftrightarrow a^2+b^2 \ge 2ab\)
\(\Leftrightarrow 2(a^2+b^2) \ge a^2+2ab+b^2\)
\(\Leftrightarrow 2(a^2+b^2) \ge (a+b)^2(đpcm)\)
b) có: \(\left.\begin{matrix}
(a-b)^2 \ge0\\ (b-c)^2 \ge0
\\ (c-a)^2 \ge0
\end{matrix}\right\}\)\(\Rightarrow (a-b)^2+(b-c)^2+(c-a)^2 \ge0\)
\(\Leftrightarrow a^2-2ab+b^2+b^2-2bc+c^2+c^2-2ca+a^2 \ge0\)
\(\Leftrightarrow 2(a^2+b^2+c^2) \ge 2ab+2bc+2ca\)
\(\Leftrightarrow 3(a^2+b^2+c^2) \ge a^2+b^2+c^2+2ab+2bc+2ca=(a+b+c)^2\)
Chúc bạn học tốt!