Question

(a²-1) (a²-4)(a²- 7)(a²- 10)< 0

tìm a bằng cách lập bảng xét dấu

Answer 1

=>(a^4-11a^2+10)(a^4-11a^2+28)<0

Đặt a^4-11a^2=x

=>(x+10)(x+28)<0

=>-28<x<10

=>-28<a^4-11a^2<10

=>\(\left\{{}\begin{matrix}a^4-11a^2+28>0\\a^2-11a^2-10< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}a^2>7\\a^2< 4\end{matrix}\right.\\\dfrac{11-\sqrt{161}}{2}< a^2< \dfrac{11+\sqrt{161}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a\in\left(-\infty;-7\right)\cup\left(7;+\infty\right)\cup\left(-2;2\right)\\0< a^2< \dfrac{11+\sqrt{161}}{2}\end{matrix}\right.\)

\(a\in\varnothing\)