a) Bpt<=>\(x^2-2\left(1+\sqrt{2}\right)x+\left(1+\sqrt{2}\right)^2>0\)
<=>\(\left(x-1-\sqrt{2}\right)^2>0\)
<=>\(x-1-\sqrt{2}\ne0\)
<=>\(x\ne1+\sqrt{2}\)
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 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 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 , \(f\left(x\right)=\frac{10-x}{5+x^2}-\frac{1}{2}\)
Lập bảng xét dấu các biểu thức sau :
a. \(f\left(x\right)=\left(3x^2-10x+3\right)\left(4x-5\right)\)
b. \(f\left(x\right)=\left(3x^2-4x\right)\left(2x^2-x-1\right)\)
c. \(f\left(x\right)=\left(4x^2-1\right)\left(-8x^2+x-3\right)\left(2x+9\right)\)
d. \(f\left(x\right)=\dfrac{\left(3x^2-x\right)\left(3-x^2\right)}{4x^2+x-3}\)
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) \(x^4\ge\left(x^2+4x+2\right)^27x^2-7x+10< 0\)
1. giải các hệ bất phương trình sau :
a, \(\left\{{}\begin{matrix}4x^2-5x-6\le0\\\left(1-x^2\right)\left(4x^2-12x+5\right)>0\end{matrix}\right.\)
b, \(-3\le\frac{x^2-3x-1}{x^2+x+1}< 3\)
1. Giải các phương trình sau :
a, \(\frac{x^2-4x+4}{x^2-2x+1}+\frac{\left|2x-4\right|}{\left|x-1\right|}-3=0\)
b, \(\left|x^2-5\right|x\left|+4\right|=\left|2x^2-3\right|x\left|+1\right|\)
Giải các bất phương trình sau:
a) \(\sqrt{2-|x-2|}>x-2\)
b) \(x^2+3x+2\geq 2\sqrt{x^2+3x+5}\)
c) \(4\sqrt{x}+\frac{2}{\sqrt{x}}<2x+\frac{1}{2x}+2\)
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 , \(f\left(x\right)=\left(1-\sqrt{2}\right)x^2-2x+1+\sqrt{2}\)
