a) \(x^2-6x+11=x^2-2.3.x+3^3+2=\left(x-3\right)^2+2\ge2\)
\(\Rightarrow\) min = \(2\) khi \(\left(x-3\right)^2=0\Leftrightarrow x-3=0\Leftrightarrow x=3\)
b) \(x^2-20x+101\Leftrightarrow x^2-2.10.x+10^2+1\Leftrightarrow\left(x-10\right)^2+1\ge1\)
\(\Rightarrow\) min \(=1\) khi \(\left(x-10\right)^2=0\Leftrightarrow x-10=0\Leftrightarrow x=10\)
d) \(x^2-2x+y^2+4y+8\) \(\Leftrightarrow\) \(x^2-2x+1^2+y^2+4y+2^2+3\)
\(\Leftrightarrow\) \(\left(x-1\right)^2+\left(y+2\right)^2+3\ge3\)
\(\Rightarrow\) min = \(3\) khi \(\left\{{}\begin{matrix}\left(x-1\right)^2=0\\\left(y+2\right)^2=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x-1=0\\y+2=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
e) \(x^2-4x+y^2-8y+6\) \(\Leftrightarrow\) \(x^2-4x+2^2+y^2-8y+4^2-14\)
\(\Leftrightarrow\) \(\left(x-2\right)^2+\left(y-4\right)^2-14\ge-14\)
vậy min = \(-14\) khi \(\left\{{}\begin{matrix}\left(x-2\right)^2=0\\\left(y-4\right)^2=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x-2=0\\y-4=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\y=4\end{matrix}\right.\)
Mình làm câu f luôn
\(F=x^2-4xy+5y^2+10x-22y+28\)
\(\Leftrightarrow F=x^2-4xy+10x+5y^2-22y+28\)
\(\Leftrightarrow F=x^2-2x.\left(2y-5\right)+\dfrac{\left(2y-5\right)^2}{4}+5y^2-\dfrac{\left(2y-5\right)^2}{4}-22y+28\)
\(\Leftrightarrow F=\left(x-\dfrac{2y-5}{2}\right)^2+20y^2-\left(4y^2-20y+25\right)-88y+112\)
Rồi cứ phân tích ra, mình bận rồi ,xin lỗi nhiều
a) \(x^2-6x+11\)\(=\left(x-3\right)^2+2\ge2\)
\(\Rightarrow GTNN=2\)
Khi x = 3