Question

[Fan Hero]

Xác định điều kiện mà số hữu tỉ x phải thỏa mãn đề bài:     a) (2x-1).x > 0                 b) x+3/x-1 < 0     c) x2-2/5x < 0                  d) (x-3).(x+7) > 0

Answer 1

[Nguyễn Lê Phước Thịnh]

1: (2x-1)*x>0

TH1: \(\left\{{}\begin{matrix}2x-1>0\\x>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>\dfrac{1}{2}\\x>0\end{matrix}\right.\Leftrightarrow x>\dfrac{1}{2}\)

TH2: \(\left\{{}\begin{matrix}2x-1< 0\\x< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x< \dfrac{1}{2}\\x< 0\end{matrix}\right.\)

=>x<0

2: 
ĐKXĐ: x<>1

\(\dfrac{x+3}{x-1}< 0\)

TH1: \(\left\{{}\begin{matrix}x+3>0\\x-1< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>-3\\x< 1\end{matrix}\right.\)

=>-3<x<1

TH2: \(\left\{{}\begin{matrix}x+3< 0\\x-1>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x< -3\\x>1\end{matrix}\right.\)

=>Loại

c: 

ĐKXĐ: x<>0

\(\dfrac{x^2-2}{5x}< 0\)

TH1: \(\left\{{}\begin{matrix}x^2-2< 0\\5x>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x^2< 2\\x>0\end{matrix}\right.\Leftrightarrow0< x< \sqrt{2}\)

TH2: \(\left\{{}\begin{matrix}x^2-2>0\\5x< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x^2>2\\x< 0\end{matrix}\right.\Leftrightarrow-\sqrt{2}< x< 0\)

d: (x-3)(x+7)>0

TH1: \(\left\{{}\begin{matrix}x-3>0\\x+7>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>3\\x>-7\end{matrix}\right.\Leftrightarrow x>3\)

TH2: \(\left\{{}\begin{matrix}x-3< 0\\x+7< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< 3\\x< -7\end{matrix}\right.\)

=>x<-7