Question

[Phạm Hoàng Hải]

Tim so nguyen x biet

(x - 2)(x² + 1) > 0

(x + 5)(2 - x) < 0

Answer 1

[Nobi Nobita]

a) Vì \(x^2\ge0\forall x\)\(\Rightarrow x^2+1\ge1\forall x\)

\(\Rightarrow\left(x-2\right)\left(x^2+1\right)>0\)\(\Leftrightarrow x-2>0\)\(\Leftrightarrow x>2\)

Vậy \(x>2\)

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

TH1: \(\hept{\begin{cases}x+5>0\\2-x< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x>-5\\2< x\end{cases}}\Leftrightarrow\hept{\begin{cases}x>-5\\x>2\end{cases}}\Leftrightarrow x>2\)

TH2: \(\hept{\begin{cases}x+5< 0\\2-x>0\end{cases}}\Leftrightarrow\hept{\begin{cases}x< -5\\2>x\end{cases}}\Leftrightarrow\hept{\begin{cases}x< -5\\x< 2\end{cases}}\Leftrightarrow x< -5\)

Vậy \(x< -5\)hoặc \(x>2\)