Question

Tìm số hữu tỉ biết:

a, ( x+2)(x+5)<0

b, (2x+5)(2x-1)<0

Answer 1

\(\left(x+2\right)\left(x+5\right)< 0\)

Với mọi \(x\in R\) thì

\(x+2< x+5\)

\(\left\{{}\begin{matrix}x+2< 0\Rightarrow x< -2\\x+5>0\Rightarrow x>-5\end{matrix}\right.\)
Vậy \(-5< x< -2\)

\(\left(2x+5\right)\left(2x-1\right)< 0\)

Với mọi \(x\in R\) thì:

\(2x-1< 2x+5\)

Nên:

\(\left\{{}\begin{matrix}2x-1< 0\Rightarrow x< \dfrac{1}{2}\\2x+5>0\Rightarrow x>-\dfrac{5}{2}\end{matrix}\right.\)

Vậy \(-\dfrac{5}{2}< x< \dfrac{1}{2}\)