Question

chứng minh đa thức > 0 với \(\forall\) x,y :

B= \(4x^2+y^2+12x-4xy-6y+16\)

Answer 1

ta có 

B=\(4x^2+y^2+9-4xy+12x-6y+7=\left(2x-y+3\right)^2+7>0\left(ĐPCM\right)\)

Answer 2

Ta có: 

\(B=4x^2+y^2+12x-4xy-6y+16\)

\(\Leftrightarrow B=4x^2+y^2+9-4xy+12x-6y+7\)

\(\Leftrightarrow B=\left(2x-y+3\right)^2+7\)

Mà \(\left(2x-y+3\right)^2\ge0\Rightarrow\left(2x-y+3\right)^2+7>0\)