A = 2x2 + 2x + 2xy + y2 + 2
A = x2 + 2xy +y2 + x2 + 2x + 1 + 1
A = (x + y)2 + (x + 1)2 + 1 \(\ge\) 1 > 0
=> A > 0 ( \(\forall\) x,y)
=> đpcm
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\(A=2x^2+2x+2xy+y^2+2\)
\(=\left(x^2+2x+1\right)+\left(x^2+2xy+y^2\right)+1\)
\(=\left(x+1\right)^2+\left(x+y\right)^2+1\)
vì \(\left(x+1\right)^2\ge0\)
\(\left(x+y\right)^2\ge0\)
\(1>0\)
\(\Rightarrow\left(x+1\right)^2+\left(x+y\right)^2+1=A>0\)
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