5x2+10y2−6xy−4x−2y+35x2+10y2−6xy−4x−2y+3

=x2−6xy+9y2+4x2−4x+1+y2−2y+1+1=x2−6xy+9y2+4x2−4x+1+y2−2y+1+1

=x2−3xy−3xy+9y2+4x2−2x−2x+1+y2−y−y+1+1=x2−3xy−3xy+9y2+4x2−2x−2x+1+y2−y−y+1+1

=x(x−3y)−3y(x−3y)+2x(2x−1)−(2x−1)+y(y−1)−(y−1)+1=x(x−3y)−3y(x−3y)+2x(2x−1)−(2x−1)+y(y−1)−(y−1)+1

=(x−3y)2+(2x−1)2+(y−1)2+1=(x−3y)2+(2x−1)2+(y−1)2+1

Với mọi giá trị của x;y∈Rx;y∈R ta có:

(x−3y)2+(2x−1)2+(y−1)2≥0(x−3y)2+(2x−1)2+(y−1)2≥0

⇒(x−3y)2+(2x−1)2+(y−1)2+1≥1⇒(x−3y)2+(2x−1)2+(y−1)2+1≥1

Vậy..............

Chúc bạn học tốt!!!