a) Cho các số thực \(a,\,\,b,\,\,c\) thỏa mãn \(\frac{a}{{b - c}} + \frac{b}{{c - a}} + \frac{c}{{a - b}} = 0\). Chứng minh rằng:
\(\frac{a}{{{{\left( {b - c} \right)}^2}}} + \frac{b}{{{{\left( {c - a} \right)}^2}}} + \frac{c}{{{{\left( {a - b} \right)}^2}}} = 0\)
b) Tìm tất cả các bộ ba số nguyên dương \(\left( {a;\,\,b;\,\,c} \right)\) thỏa mãn:
\(a \le b \le c\) và \(\left( {1 + \frac{1}{a}} \right)\left( {1 + \frac{1}{b}} \right)\left( {1 + \frac{1}{c}} \right) = 2\).
A.\(\left( {a;b;c} \right) \in \left\{ {,\left( {2;\,\,5;\,\,9} \right),\,\,\left( {2;\,\,6;\,\,7} \right),\left( {3;\,\,3;\,\,8} \right),\,\,\left( {3;\,\,4;\,\,5} \right)} \right\}\).
B.\(\left( {a;b;c} \right) \in \left\{ {,\left( {2;\,\,5;\,\,9} \right),\,\,\left( {2;\,\,6;\,\,7} \right),\,\,\left( {3;\,\,4;\,\,5} \right)} \right\}\).
C.\(\left( {a;b;c} \right) \in \left\{ {\left( {2;\,\,4;\,\,15} \right),\,\,\left( {2;\,\,5;\,\,9} \right),\,\,\left( {2;\,\,6;\,\,7} \right),\,\,\left( {3;\,\,4;\,\,5} \right)} \right\}\).
D.\(\left( {a;b;c} \right) \in \left\{ {\left( {2;\,\,4;\,\,15} \right),\,\,\left( {2;\,\,5;\,\,9} \right),\,\,\left( {2;\,\,6;\,\,7} \right),\left( {3;\,\,3;\,\,8} \right),\,\,\left( {3;\,\,4;\,\,5} \right)} \right\}\).
