`A=x(x-6)+10`
`=x^2-6x+10`
`=(x-3)^2+1>=1>0AAx`
`<=>A>0AAx`
`B=x^2-2x+9y^2-6+3`
`=x^2-2x+1+9y^2-6y+1+1`
`=(x-1)^2+(3y-1)^2+1>=1>0AAx,y`
`<=>B>0AAx,y`.
\(A=x\left(x-6\right)+10\\ A=x^2-6x+10\\ A=\left(x^2-6x+9\right)+1\\ A=\left(x-3\right)^2+1\)
\(\left(x-3\right)^2\ge0\forall x\\ \Rightarrow A=\left(x-3\right)^2+1\ge1\forall x\\ \Rightarrow A>0\forall x\)
______________________________
\(B=x^2-2x+9y^2-6y+3\\ B=\left(x^2-2x+1\right)+\left(9y^2-6y+1\right)+1\\ B=\left(x-1\right)^2+\left(3y-1\right)^2+1\)
\(\left(x-1\right)^2\ge0\forall x\\ \left(3y-1\right)^2\ge0\forall y\\ \Rightarrow B=\left(x-1\right)^2+\left(3y-1\right)^2+1\ge1\forall x;y\\ \Rightarrow B>0\forall x;y\)
