*Tìm GTNN:
Ta có:
$P=\dfrac{x^2+1}{x^2-x+1}=\dfrac{3x^2+3}{3(x^2-x+1)}=\dfrac{x^2+2x+1+2(x^2-x+1)}{3(x^2-x+1)}\\=\dfrac{(x+1)^2}{3(x^2-x+1)}+\dfrac{2}{3}\geq \dfrac{2}{3}$
Dấu "=" xảy ra <=> x=-1
Vậy Min P=2/3 <=> x=-1
*Tìm GTLN:
Ta có:
$P=\dfrac{x^2+1}{x^2-x+1}=\dfrac{2x^2-2x+2-x^2+2x-1}{x^2-x+1}=\dfrac{2(x^2-x+1)-(x^2-2x+1)}{x^2-x+1}\\=2-\dfrac{(x-1)^2}{x^2-x+1}\leq 2$
Dấu "=" xảy ra <=> x=1
Vậy Max P=2 <=> x=1