Question

[Hoàng Thị Ngọc Cầm]

Tìm GTNN của biểu thức :

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

Answer 1

[KAl(SO4)2·12H2O]

\(\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)\)

\(=\left[\left(x+1\right)\left(x-6\right)\right]\left[\left(x-2\right)\left(x-3\right)\right]\)

\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)

\(=\left(x^2+5x\right)^2-36\ge-36\)

\(\Rightarrow\text{MIN}_{-36}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)