+ Rút gọn A
\(A=\dfrac{x^2}{x-2}\left(\dfrac{x^2+4}{x}-4\right)+3\)
\(A=\dfrac{x^2}{x-2}.\dfrac{x^2+4}{x}-4.\dfrac{x^2}{x-2}+3\)
\(A=\dfrac{x^4+4x^2}{x^2-2x}-\dfrac{4x^2}{x-2}+3\)
\(A=\dfrac{x^4+4x^2}{x^2-2x}-\dfrac{4x^3}{x^2-2x}+3\)
\(A=\dfrac{x^4-4x^3+4x^2}{x^2-2x}+3\)
\(A=\dfrac{x^4-2x^3-2x^3+4x^2}{x\left(x-2\right)}+3\)
\(A=\dfrac{x^3\left(x-2\right)-2x^2\left(x-2\right)}{x\left(x-2\right)}+3\)
\(A=\dfrac{x\left(x-2\right)\left(x^2-2x\right)}{x\left(x-2\right)}+3\)
\(A=x^2-2x+3\)
+ Tìm GTNN của A
Ta có: \(A=x^2-2x+3\)
\(A=\left(x^2-2x+1\right)+2\)
\(A=\left(x-1\right)^2+2\)
Vì \(\left(x-1\right)^2\ge0\) với mọi x
\(\Rightarrow\left(x-1\right)^2+2\ge2\) với mọi x
\(\Rightarrow Amin=2\Leftrightarrow x=1\)
