\(P=a^2+a+1\)
\(=a^2+\frac{1}{2}\cdot2\cdot a+\frac{1}{4}+\frac{3}{4}\)
\(=\left(a+\frac{1}{2}\right)^2+\frac{3}{4}\)
\(\left(a+\frac{1}{2}\right)^2\ge0\Rightarrow\left(a+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)
\(\Rightarrow P\ge\frac{3}{4}\)
dấu "=" xảy ra khi :
\(\left(a+\frac{1}{2}\right)^2=0\Rightarrow a+\frac{1}{2}=0\Rightarrow a=-\frac{1}{2}\)
vậy