Question

Tìm GTLN,GTNN của biểu thức:

A=(x-1)(x+2)(x+3)(x+6)

Answer 1

Answer 2

\(A=\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)\\ =\left(x-1\right)\left(x+6\right)\left(x+2\right)\left(x+3\right)\\ =\left(x^2+5x-6\right)\left(x^2+5x+6\right)\\ =\left(x^2+5x\right)^2-36\ge-36\)

Dấu "=" xảy ra khi x^2+5x=0

\(\Rightarrow x\left(x+5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)

Min A = -36 khi x=0 hoặc x=-5