a)\(A=\left(x-5\right)^2\ge0\)
\(\Rightarrow Min=0\)dấu \(=\)xảy ra khi \(x=5\)
a) \(A=x^2-10x+25\)
\(A=\left(x^2-10x+25\right)+0\)
\(A=\left(x-5\right)^2+0\)
Mà \(\left(x-5\right)^2\ge0\forall x\)
\(\Rightarrow A\ge0\)
Dấu "=" xảy ra khi : \(x-5=0\Leftrightarrow x=5\)
Vậy ...
b) \(B=x^2+y^2-x+6y+10\)
\(B=\left(x^2-x+\frac{1}{4}\right)+\left(y^2+6y+9\right)+\frac{3}{4}\)
\(B=\left(x-\frac{1}{2}\right)^2+\left(y+3\right)^2+\frac{3}{4}\)
Mà \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)
\(\left(y+3\right)^2\ge0\forall y\)
\(\Rightarrow B\ge\frac{3}{4}\)
Dấu "=" xảy ra khi : \(\hept{\begin{cases}x-\frac{1}{2}=0\\y+3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=-3\end{cases}}\)
Vậy ...
c) \(C=2x^2-6x+10\)
\(C=2\left(x^2-3x+\frac{9}{4}\right)+\frac{11}{2}\)
\(C=2\left(x-\frac{3}{2}\right)^2+\frac{11}{2}\)
Mà \(\left(x-\frac{3}{2}\right)^2\ge0\forall x\) \(\Rightarrow2\left(x-\frac{3}{2}\right)^2\ge0\forall x\)
\(\Rightarrow C\ge\frac{11}{2}\)
Dấu "=" xảy ra khi :
\(x-\frac{3}{2}=0\Leftrightarrow x=\frac{3}{2}\)
Vậy ...
