M2(n2+4)-4m2n+ 2mn-4m+1>=0 Доказать

Question

M2(n2+4)-4m2n+ 2mn-4m+1>=0 Доказать

---

Answer 1

M²*(n²+4)-4m²n+2mn-4m+1=m²n²+4m²-4m²n+2mn-4m+1=
=(m²n²+2mn+1)-(4m²n+4m)+4m²=(mn+1)²-4m*(mn+1)+(2m)²=
=(mn+1)²-2*2m*(mn+1)+(2m)²=(mn+1-2m)²≡>0.