a.
\(x^2+xy+y^2+1=\left(x+\dfrac{y}{2}\right)^2+\dfrac{3y^2}{4}+1>0\) ; \(\forall x;y\)
b.
\(x^2+5y^2+2x-4xy-10y+14\)
\(=\left(x^2+4y^2+1-4xy+2x-4y\right)+\left(y^2-6y+9\right)+4\)
\(=\left(x-2y+1\right)^2+\left(y-3\right)^2+4>0\) ; \(\forall x;y\)
c.
\(5x^2+10y^2-6xy-4x-2y+3\)
\(=\left(x^2-6xy+9y^2\right)+\left(4x^2-4x+1\right)+\left(y^2-2y+1\right)+1\)
\(=\left(x-3y\right)^2+\left(2x-1\right)^2+\left(y-1\right)^2+1>0\) ; \(\forall x;y\)
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