\(\dfrac{x}{2}-\dfrac{1}{x}=\dfrac{1}{12}\) (ĐK: \(x\ne0\))
\(\Rightarrow\dfrac{x^2}{2x}-\dfrac{2}{2x}=\dfrac{1}{12}\)
\(\Rightarrow\dfrac{x^2-2}{2x}=\dfrac{1}{12}\)
\(\Rightarrow12\left(x^2-2\right)=2x\)
\(\Rightarrow12x^2-24=2x\)
\(\Rightarrow12x^2-2x-24=0\)
\(\Rightarrow2\left(6x^2-x-12\right)=0\)
\(\Rightarrow2\left(6x^2+8x-9x-12\right)=0\)
\(\Rightarrow2\left[2x\left(3x+4\right)-3\left(3x+4\right)\right]=0\)
\(\Rightarrow2\left(3x+4\right)\left(2x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3x=-4\\2x=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{4}{3}\left(tm\right)\\x=\dfrac{3}{2}\left(tm\right)\end{matrix}\right.\)
Vậy: \(S=\left\{-\dfrac{4}{3};\dfrac{3}{2}\right\}\)
\(\dfrac{x}{2}-\dfrac{1}{x}=\dfrac{1}{12}\)
\(\Rightarrow\dfrac{x^2}{2x}-\dfrac{2}{2x}=\dfrac{1}{12}\)
\(\Rightarrow\dfrac{x^2-2}{2x}=\dfrac{1}{12}\)
\(\Rightarrow12\left(x^2-2\right)=2x\)
\(\Rightarrow12x^2-2x-24=0\)
\(\Rightarrow12x^2-18x+16x-24=0\)
\(\Rightarrow6x\left(2x-3\right)+8\left(2x-3\right)=0\)
\(\Rightarrow\left(2x-3\right)\left(6x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\6x+8=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{4}{3}\end{matrix}\right.\)
`x/2-1/x=1/12`
\(\Rightarrow\dfrac{x.6x}{12x}-\dfrac{12}{12x}=\dfrac{x}{12x}\\ \Rightarrow\dfrac{6x^2-12-x}{12x}=0\\ \Rightarrow\dfrac{6x^2-12+8x-9x}{12x}=0\\ \Rightarrow\dfrac{\left(6x^2+8x\right)-\left(9x+12\right)}{12x}=0\\ \Rightarrow\dfrac{2x\left(3x+4\right)-3\left(3x+4\right)}{12x}=0\\ \Rightarrow\left(3x+4\right)\left(2x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x+4=0\\2x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}3x=-4\\2x=3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=\dfrac{3}{2}\end{matrix}\right.\)
Cậu đã học dạng này chưa nhỉ?
x/2 - 1/x = 1/12 (ĐKXĐ: x ≠ 0)
6x² - 12 = x
6x² - x - 12 = 0
6x² - 9x + 8x - 12 = 0
(6x² - 9x) + (8x - 12) = 0
3x(2x - 3) + 4(2x - 3) = 0
(2x - 3)(3x + 4) = 0
2x - 3 = 0 hoặc 3x + 4 = 0
*) 2x - 3 = 0
2x = 3
x = 3/2 (nhận)
*) 3x + 4 = 0
3x = -4
x = -4/3 (nhận)
Vậy x = -4/3; x = 3/2
