Ta có :
\(F=\frac{-x^2+x-10}{x^2-2x+1}=\frac{-\left(x^2-x+10\right)}{\left(x-1\right)^2}=\frac{-\left(x-\frac{1}{2}\right)^2-\frac{19}{2}}{\left(x-1\right)^2}\)
Với mọi x ta có :
\(\left(x-\frac{1}{2}\right)^2\ge0\)
\(\Leftrightarrow-\left(x-\frac{1}{2}\right)^2\le0\)
\(\Leftrightarrow-\left(x-\frac{1}{2}\right)^2-\frac{19}{2}\le-\frac{19}{2}\)
Lại có : \(\left(x-1\right)^2\ge1\)
\(\Leftrightarrow\frac{-\left(x-\frac{1}{2}\right)^2-\frac{19}{2}}{\left(x-1\right)^2}\le-\frac{19}{2}\)
\(\Leftrightarrow F\le-\frac{19}{2}\)
Dấu "=" xảy ra \(\Leftrightarrow x=\frac{1}{2}\)
Vậy..
