\(A=\dfrac{-x^4+5x^3-5x^2-2x+3}{x^2-4x+2}\)
\(=\dfrac{-x^4+4x^3-2x^2+x^3-4x^2+2x+x^2-4x+2+1}{x^2-4x+2}\)
\(=-x^2+x+1+\dfrac{1}{x^2-4x+2}\)
\(C=-x^2+x+1\)
\(=-\left(x^2-x-1\right)\)
\(=-\left(x^2-x+\dfrac{1}{4}-\dfrac{5}{4}\right)\)
\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}< =\dfrac{5}{4}\)
Dấu = xảy ra khi x=1/2