a) \(P=x^2-2x+5\)
\(=x^2-2x+1+4\)
\(=\left(x-1\right)^2+4\ge4\)
\(MinP=4\Leftrightarrow x-1=0\Rightarrow x=1\)
b) \(Q=2x^2-6x\)
\(=2\left(x^2-3x\right)\)
\(=2\left(x^2-2.x.\frac{3}{2}+\frac{9}{4}-\frac{9}{4}\right)\)
\(=2\left(\left(x-\frac{3}{2}\right)^2-\frac{9}{4}\right)\)
\(=-\frac{9}{2}-2\left(x-\frac{3}{2}\right)^2\le\frac{-9}{2}\)
\(MinQ=\frac{-9}{2}\Leftrightarrow x-\frac{3}{2}=0\Rightarrow x=\frac{3}{2}\)
M=x^2+y^2-x+6y+10
M=(x^2-x+1/4)+(y^2+6y+9)+3/4
M=(x-1/2)^2+(y+3)^2+3/4
\(minM=\frac{3}{4}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=-3\end{cases}}\)
