hanhtrinhtuonglai

$\fn_phv {\frac {a}{b+c}}+{\frac {b}{c+d}}+{\frac {c}{d+a}}+{\frac {d}{a+b}}={ \frac {{a}^{2}}{{\it ab}+{\it ac}}}+{\frac {{b}^{2}}{{\it bc}+{\it bd} }}+{\frac {{c}^{2}}{{\it cd}+{\it ac}}}+{\frac {{d}^{2}}{{\it ad}+{ \it bd}}}\geq {\frac { \left( a+b+c+d \right) ^{2}}{{\it ab}+2\,{\it ac}+{\it ad}+{ \it bc}+2\,{\it bd}+{\it cd}}}\geq 2 \Leftrightarrow {a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}\geq 2\,{\it ac}+2\,{\it bd}$