Question

Докажите неравенство 49b2-14bc+2c2+16c+69>0

Answer 1

$49b^2-14bc+2c^2+16c+69=\\ \\ (49b^2-14bc+c^2)+(c^2+16c+64)+5=\\ \\ (7b-c)^2+(c+8)^2+5>0\\ \\ (7b-c)^2\geq 0;(c+8)^2\geq 0;5>0$