a/ ĐKXĐ:...
\(\Leftrightarrow\frac{\left(x-2\right)^2}{\left(x-1\right)^2}+2\left|\frac{x-2}{x-1}\right|-3=0\)
\(\Leftrightarrow\left|\frac{x-2}{x-1}\right|^2+2\left|\frac{x-2}{x-1}\right|-3=0\)
Đặt \(\left|\frac{x-2}{x-1}\right|=t\left(t\ge0\right)\)
\(\Rightarrow pt\Leftrightarrow t^2+2t-3=0\Leftrightarrow\left[{}\begin{matrix}t=1\\t=-3\left(l\right)\end{matrix}\right.\)
Ok tự giải nốt
b/ viết lại đề bài đi cậu
Bài 3 : Xét dấu biểu thức sau :
1 , \(f\left(x\right)=\frac{x-7}{4x^2-19x+12}\)
2 , \(f\left(x\right)=\frac{11x+3}{-x^2+5x-7}\)
3 , \(f\left(x\right)=\frac{3x-2}{x^3-3x^2+2}\)
4 , \(f\left(x\right)=\frac{x^2+4x-12}{\sqrt{6}x^2+3x+\sqrt{2}}\)
5 , \(f\left(x\right)=\frac{x^2-3x-2}{-x^2+x-1}\)
6 , \(f\left(x\right)=\frac{x^3-5x+4}{x^4-4x^3+8x-5}\)
7 , \(f\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)\left(-2x^2+x-1\right)}{\left(2x-5\right)\left(x^2+3x-10\right)}\)
8 , \(f\left(x\right)=\left(-x^2+x-1\right)\left(6x^2-5x+1\right)\)
9 , \(f\left(x\right)=\frac{x^2-x-2}{-x^2+3x+4}\)
10 , \(f\left(x\right)=\left(x^2-5x+4\right)\left(2-5x+2x^2\right)\)
Bài 4 Xét dấu biểu thức sau
1 , \(f\left(x\right)=x^2-3x-2-\frac{8}{x^2-3x}\)
2 , \(f\left(x\right)=\frac{1}{x+1}-\frac{1}{x}-\frac{1}{2}\)
3 , \(f\left(x\right)=\frac{x^2-4x+3}{3-2x}-1+x\)
4 , \(f\left(x\right)=\frac{x^2-1}{\left(x^2-3\right)\left(-3x^2+2x+8\right)}\)
5 , \(f\left(x\right)=x^4-5x^2+2x+3\)
6 , \(f\left(x\right)=\frac{x^2+4x+15}{x^2-1}-\frac{x-3}{x+1}-\frac{x-2}{1-x}\)
bài 1: giải hệ bất phương trình sau:
a) \(\left\{{}\begin{matrix}2-x>0\\2x+1>x-2\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}3\left(x-6\right)< -3\\\frac{5x+1}{2}>7\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\frac{x-2}{x-1}\le0\\\left(x-1\right)\left(x+1\right)\le0\end{matrix}\right.\)
bài 2: xét dấu các nhị thức sau:
a) q(x)=\(\frac{\left(x-1\right)\left(2x-7\right)}{\left(2+x\right)^2}\)
b) n(x)=\(\frac{\left(1-2x\right)\left(2x-1\right)}{3+x}\)
bài 3: giải các bất phương trình sau;
a) 2\(\left|x-3\right|-\left|3x+1\right|\le x+5\)
b) \(\left|\frac{3x+1}{x-3}\right|< 3\)
1) \(\frac{x^2+2x+5}{x+4}\ge x-3\)
2) \(\frac{x^2-3x-1}{2-x}>-x\)
3) \(\frac{3x-47}{3x-1}>\frac{4x-47}{2x-1}\)
4) \(x+\frac{9}{x+2}\ge4\)
5) \(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\)
6) \(x^4\ge\left(x^2+4x+2\right)^27x^2-7x+10< 0\)
Giải các bất phương trình sau :
a) \(\left\{{}\begin{matrix}x^2\ge0,25\\x^2-x\le0\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\left(x-1\right)\left(2x+3\right)>0\\\left(x-4\right)\left(x+\dfrac{1}{4}\right)\le0\end{matrix}\right.\)
Bài 2 Xét dấu biểu thức sau
1 , \(f\left(x\right)=x^2-\sqrt{3}x+\frac{3}{4}\)
2 , \(f\left(x\right)=-x^2+3x-2\)
3 , \(f\left(x\right)=x^4-4x+1\)
4 , \(f\left(x\right)=\frac{3x+7}{x^2-x-2}\)
5 , \(f\left(x\right)=\frac{x+2}{3x+1}-\frac{x-2}{2x-1}\)
6 , \(f\left(x\right)=\frac{1}{x^2-5x+4}-\frac{1}{x^2-7x+10}\)
7 , \(f\left(x\right)=\left(x-1\right)\left(x-3\right)-\frac{18}{x^2-4x-4}\)
8 , \(f\left(x\right)=\left(x^2-1\right)\left(x-2\right)\)
9 , \(f\left(x\right)=\left(x+3\right)\left(-4x^2+9x-2\right)\)
10 , \(f\left(x\right)=\frac{10-x}{5+x^2}-\frac{1}{2}\)
1. giải các hệ bất phương trình sau
a. \(\left\{{}\begin{matrix}\frac{2x+3}{x-1}\ge1\\\frac{\left(x+2\right)\left(2x-4\right)}{x-1}\le0\end{matrix}\right.\)
1. Xét dấu các biểu thức sau :
a, f(x) = \(\frac{\left(7-4x\right)\left(x^2+x-2\right)}{2x^2-3x+2}\)
b, g(x) = \(\frac{\left(25-x^2\right)\left(x^2+6x+9\right)}{-x^2-2x+8}\)
c, h(x) = \(\frac{x\left(x^2-4x-12\right)}{\sqrt{6}x^2-3x+\sqrt{2}}\)
d, k(x) = \(\frac{-x^3-5x^2+4}{x^4+4x^3-8x-5}\)
Bài 1 Xét dấu biểu thức sau
1 , \(f\left(x\right)=2x^2-x+1\)
2 , \(f\left(x\right)=-2x^2+5x+7\)
3 , \(f\left(x\right)=9x^2-12x+4\)
4 , \(f\left(x\right)=2x^2+2x+5\)
5 , \(f\left(x\right)=2x^2+2\sqrt{2}x+1\)
6 , \(f\left(x\right)=-4x^2-4x+1\)
7 , \(f\left(x\right)=\sqrt{3}x+\left(\sqrt{3}+1\right)x+1\)
8 , \(f\left(x\right)=x^2+\left(\sqrt{5}-1\right)x-\sqrt{5}\)
9 , \(f\left(x\right)=x^2-\left(\sqrt{7}-1\right)+\sqrt{3}\)
10 , \(f\left(x\right)=\left(1-\sqrt{2}\right)x^2-2x+1+\sqrt{2}\)