\(A=x^6+2x\left(x^2+y\right)+x^2+y^2+26\)
\(=x^6+2x^2+2xy+x^2+y^2+26\)
\(=x^6+2x^2+\left(x+y\right)^2+26\ge26\forall x;y\)
Dấu "=" xảy ra<=> \(x=0\) và \(\left(x+y\right)^2=0\Rightarrow y=0\)
Vậy Amin =26 tại x=y=0
B=\(y^2-2xy+3x^2+2y-14x+1949\)
\(=\left(y^2-2xy+x^2+2y-2x+1\right)+\left(2x^2-12x+18\right)+1930\)
\(=\left(x-y-1\right)^2+2\left(x-3\right)^2+1930\)
\(\ge1930\)
MinB=1930 khi \(\hept{\begin{cases}x=y+1\\x=3\end{cases}\Rightarrow\hept{\begin{cases}x=3\\y=2\end{cases}}}\)
D=\(x\left(x-1\right)\left(x-2\right)\left(x-3\right)\)
\(=\left(x^2-3x\right)\left(x^2-3x+2\right)\)
\(=\left(x^2-3x\right)^2+2\left(x^2-3x\right)+1-1\)
\(=\left(x^2-3x+1\right)^2-1\ge-1\)
MinD=-1 khi \(x^2-3x+1=0\)=> \(x=\frac{3\pm\sqrt{5}}{2}\)
