a: \(A=\dfrac{9xy^2-6x^2y}{-3xy}+\dfrac{6x^2y+2x^4}{2x^2}\)
\(=-3y+2x+3y+x^2=x^2+2x\)
\(=x^2+2x+1-1=\left(x+1\right)^2-1>=-1\forall x\)
Dấu '=' xảy ra khi x+1=0
=>x=-1
b: \(B=x^2+y^2-x+6y+10\)
\(=x^2-x+\dfrac{1}{4}+y^2+6y+9+0,75\)
\(=\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2+0,75>=0,75\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-\dfrac{1}{2}=0\\y+3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=-3\end{matrix}\right.\)
c: \(C=2x^2-6x+10\)
\(=2\left(x^2-3x+5\right)\)
\(=2\left(x^2-3x+\dfrac{9}{4}+\dfrac{11}{4}\right)\)
\(=2\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{2}>=\dfrac{11}{2}\forall x\)
Dấu '=' xảy ra khi \(x-\dfrac{3}{2}=0\)
=>\(x=\dfrac{3}{2}\)
d: \(M=x^2-4x+5\)
\(=x^2-4x+4+1\)
\(=\left(x-2\right)^2+1>=1\forall x\)
Dấu '=' xảy ra khi x-2=0
=>x=2
e: \(N=y^2-y-3\)
\(=y^2-y+\dfrac{1}{4}-\dfrac{13}{4}\)
\(=\left(y-\dfrac{1}{2}\right)^2-\dfrac{13}{4}>=-\dfrac{13}{4}\forall y\)
Dấu '=' xảy ra khi \(y-\dfrac{1}{2}=0\)
=>\(y=\dfrac{1}{2}\)
f: \(P=x^2+y^2-4x+y+7\)
\(=x^2-4x+4+y^2+y+\dfrac{1}{4}+2,75\)
=\(\left(x-2\right)^2+\left(y+\dfrac{1}{2}\right)^2+2,75>=2,75\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2=0\\y+\dfrac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-\dfrac{1}{2}\end{matrix}\right.\)
