Question

Tìm MaxA = (x^2 - x + 1)/(x^2 + x + 1)

Answer 1

là sao

Answer 2

Ta có :

\(A=\dfrac{x^2-x+1}{x^2+x+1}=\dfrac{3x^2+3x+3-2x^2-4x-2}{x^2+x+1}=\dfrac{3\left(x^2+x+1\right)-2\left(x+1\right)^2}{x^2+x+1}=3-\dfrac{2\left(x+1\right)^2}{x^2+x+1}\)

Do: \(\left\{{}\begin{matrix}2\left(x-1\right)^2\ge0\\x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\end{matrix}\right.\) \(\Rightarrow3-\dfrac{2\left(x+1\right)^2}{x^2+x+1}\le3\)

Vậy \(MAX_A=3\) . Dấu \("="\) xảy ra khi \(x=-1\)