Question

Tìm GTNN của biểu thức:

A= x² -8x +9

B= 2x² -6x +3

Answer 1

\(A=x^2-8x+16-7=\left(x-4\right)^2-7\\ \left(x-4\right)^2\ge0\Rightarrow A=\left(x-4\right)^2-7\ge-7\)

Dấu "$=$" khi $x-4=0\Rightarrow x=4$

\(B=2x^2-6x+\dfrac{9}{2}-\dfrac{3}{2}=2\left(x^2-3x+\dfrac{9}{4}\right)-\dfrac{3}{2}=2\left(x-\dfrac{3}{2}\right)^2-\dfrac{3}{2}\\ \left(x-\dfrac{3}{2}\right)^2\ge0\Rightarrow B=2\left(x-\dfrac{3}{2}\right)^2-\dfrac{3}{2}\ge-\dfrac{3}{2}\)Dấu "$=$" khi $x-\dfrac 32=0\Rightarrow x=\dfrac 32$

Answer 2

a/ -7

b/\(-\dfrac{3}{2}\)