Question

Докажите неравенство
4bc<=4b2+c2

Answer 1

$4bc leqslant 4 {b}^{2} + {c}^{2} \ - 4 {b}^{2} +4bc - {c}^{2} leqslant 0 \ 4 {b}^{2} - 4bc + {c}^{2} geqslant 0 \ {(2b - c )}^{2} geqslant 0$
Доказано!