Question

Tìm GTLN, GTNN của:

A= 5-8x-x²

B= x²+x+1

Answer 1

A= 5-8x-x²

=-x²-8x+21-16

=21-(x²+8x+16)

=21-(x+4)²\(\ge\)21-0=21

Dấu = khi x=-4

Vậy Amax=21 khi x=-4

B= x²+x+1

\(=x^2+\frac{x}{2}+\frac{x}{2}+\frac{1}{4}+\frac{3}{4}\)

\(=x\left(x+\frac{1}{2}\right)+\frac{1}{2}\left(x+\frac{1}{2}\right)+\frac{3}{4}\)

\(=\left(x+\frac{1}{2}\right)\left(x+\frac{1}{2}\right)+\frac{3}{4}\)

\(=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge0+\frac{3}{4}=\frac{3}{4}\)

Dấu = khi x=-1/2

Vậy Bmin=3/4 khi x=-1/2