Докажите неравенства a^2+2b^2+2ab+2b+2>0

Question

Докажите неравенства
a^2+2b^2+2ab+2b+2>0

Answer 1

A^2 + 2b^2 + 2ab + 2b + 2 = (a^2 + 2ab + b^2) + (b^2 + 2b + 1) + 1 = (a + b)^2 + (b + 1)^2 + 1 >= 1 > 0