N^2+m^2+12^2+3 ⩾ 2(n+m+12) Доказать неравенство

Question

N^2+m^2+12^2+3 ⩾ 2(n+m+12)

Доказать неравенство

Answer 1

N²+m²+12²+3≥2(n+m+12)
n²+m²+12²+(1+1+1)≥2n+2m+2*12
n²-2n+1+m²-2m+1+12²-2*12+1≥0
(n-1)²+(m-1)²+(12-1)²≥0
доказано