a. \(x^2-8x+19\)
\(=x^2-2.x.4+16+3\)
\(=\left(x-4\right)^2+3\ge3\forall x\)
=> đpcm
b. \(4x^2+4x+3\)
\(=\left(2x\right)^2+2.2x.1+1+2\)
\(=\left(2x+1\right)^2+2\ge2\forall x\)
=> đpcm
d, \(x^2-2xy+2y^2+2y+5\)
\(=x^2-2xy+y^2+y^2+2y+1+4\)
\(=\left(x-y\right)^2+\left(y+1\right)^2+4\)
Với mọi giá trị của x;y ta có:
\(\left(x-y\right)^2\ge0;\left(y+1\right)^2\ge0\)
\(\Rightarrow\left(x-y\right)^2+\left(y+1\right)^2+4\ge4>0\)
Vậy.............
c. \(x^2+y^2-4x+2\)
\(=\left(x-2\right)^2+y^2+2\)
Do \(\left(x-2\right)^2\ge0\forall x\)
\(y^2\ge0\forall x\)
\(\Rightarrow x^2+y^2-4x+2\ge0\forall x\)
