a, Đặt \(A=2+x-x^2=-\left(x^2-x-2\right)=-\left(x^2-x+\frac{1}{4}-\frac{9}{4}\right)=-\left(x-\frac{1}{2}\right)^2+\frac{9}{4}\)
Vì \(\left(x-\frac{1}{2}\right)^2\ge0\Rightarrow-\left(x-\frac{1}{2}\right)^2\le0\Rightarrow A=-\left(x-\frac{1}{2}\right)^2+\frac{9}{4}\le\frac{9}{4}\)
Dấu "=" xảy ra khi x = 1/2
Vậy Amax=9/4 khi x=1/2
b, Đặt \(B=4x^2-20x+26=\left(2x\right)^2-2.2x.5+25+1=\left(2x-5\right)^2+1\)
Vì \(\left(2x-5\right)^2\ge0\Rightarrow B=\left(2x-5\right)^2+1\ge1\)
Dấu "=" xảy ra khi x = 5/2
Vậy Bmin=1 khi x=5/2