Question

Bài 1 : Tìm x thuộc tập hợp Z :

a) (x² - 1) . ( x² - 4) > 0

b) 2 + 4 + 6 + .....+ 2x = 210

Answer 1

Xin lỗi, mình sai đề :

a) (x² - 1) . ( x² - 4) < 0

Answer 2

\(\text{b) }2+4+6+...+2x=210\\ \Leftrightarrow2\left(1+2+3+...+x\right)=210\\ \Leftrightarrow1+2+3+...+x=105\\ \Leftrightarrow1+2+3+...+x=1+2+3+...+14\\\Leftrightarrow\left(1+2+3+...\right)+x=\left(1+2+3+...\right)+14\\ \Leftrightarrow x=14 \)

Vậy \(x=14\)

Answer 3

\(\text{a) }\left(x^2-1\right)\left(x^2-4\right)>0\)

Để \(\left(x^2-1\right)\left(x^2-4\right)>0\)

thì \(\left(x^2-1\right)\) và \(\left(x^2-4\right)\) trái dấu

Mà \(\left(x^2-1\right)>\left(x^2-4\right)\)

\(\left\{{}\begin{matrix}x^2-1>0\\x^2-4< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2>1\\x^2< 4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x< 2\end{matrix}\right.\\\left\{{}\begin{matrix}x>-1\\x< -2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow1< x< 2\text{ hoặc }-1< x< -2\)Mà \(x\in Z\)

\(\Leftrightarrow x\in\varnothing\)

Vậy \(x\in\varnothing\)