Câu 1:

a)\(x^2-4+\left(x-2\right)\left(2x+1\right)=0\)

\(\Rightarrow x^2-4+2x^2+x-4x-2=0\)

\(\Rightarrow3x^2-3x-6=0\)

\(\Rightarrow x^2-x-2=0\)(Vì nhân tử chung là 3 thì ra bằng 0)

\(\Rightarrow x^2-2x+x-2=0\)

\(\Rightarrow\left(x+1\right)\left(x-2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

         Vậy x=-1;2

Câu 2:

a)\(ĐKXĐ:X\ne1;X\ne-1;X\ne-2;\)

b)\(\frac{x+1}{x-1}-\frac{x-1}{x+2}=\frac{3}{x^2-1}\)(\(ĐKXĐ:X\ne1;X\ne-1;X\ne-2;\))

\(\Rightarrow\frac{\left(x+1\right)^2\left(x+2\right)}{\left(x^2-1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x-1^{ }\right)^2}{\left(x^2-1\right)\left(x+2\right)}=\frac{3\left(x+2\right)}{\left(x^2-1\right)\left(x+2\right)}\)

\(\Rightarrow\left(x+1\right)^2\left(x+2\right)-\left(x+1\right)\left(x-1\right)^2=3x+6\)

\(\Rightarrow\left(x+1\right)\left[\left(x+1\right)\left(x+2\right)-\left(x-1\right)^2\right]=3x+6\)

\(\Rightarrow\left(x+1\right)\left[x^2+3x+2-x^2+2x-1\right]=3x+6\)

\(\Rightarrow\left(x+1\right)\left[5x+1\right]=3x+6\)

\(\Rightarrow5x^2+6x+1-3x-6=0\)

\(\Rightarrow5x^2+3x-5=0\)

\(\Rightarrow x=0,745\left(TM\right)\)

a)Ta có:\(1-2x=\frac{-7x-11}{5}\)

\(\Rightarrow\frac{5-10x}{5}=\frac{-7x-11}{5}\)

\(\Rightarrow5-10x=-7x-11\)

\(\Rightarrow5-10x+7x+11=0\)

\(\Rightarrow16-3x=0\)

\(\Rightarrow x=\frac{16}{3}\)

Câu 1: 

Ta có: \(\Delta=\left[-2\left(m+2\right)\right]^2-4\cdot m\cdot\left(2+3m\right)\)

\(\Leftrightarrow\Delta=\left(2m+4\right)^2-4m\left(2+3m\right)\)

\(\Leftrightarrow\Delta=4m^2+16m+16-8m-12m^2\)

\(\Leftrightarrow\Delta=-8m^2+8m+16\)

\(\Leftrightarrow\Delta=-8\left(m^2-m-2\right)\)

Để phương trình vô nghiệm thì \(\Delta< 0\)

\(\Leftrightarrow m^2-m-2>0\)

\(\Leftrightarrow\left(m-2\right)\left(m+1\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m-2>0\\m+1>0\end{matrix}\right.\\\left\{{}\begin{matrix}m-2< 0\\m+1< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m>2\\m>-1\end{matrix}\right.\\\left\{{}\begin{matrix}m< 2\\m< -1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m>2\\m< -1\end{matrix}\right.\)

Câu 1 

Để pt vô nghiệm \(\Rightarrow\Delta'=\left(m+2\right)^2-\left(3m+2\right)m=m^2+4m+4-3m^2-2m=-2m^2+2m+4=-2\left(m^2-m-2\right)=-2\left(m+1\right)\left(m-2\right)< 0\) \(\Leftrightarrow\left(m+1\right)\left(m-2\right)>0\Leftrightarrow\left[{}\begin{matrix}m< -1\\m>2\end{matrix}\right.\)

a)11x-7<8x+7

<-->11x-8x<7+7

<-->3x<14

<--->x<14/3 mà x nguyên dương 

---->x \(\in\){0;1;2;3;4}

b)x^2+2x+8/2-x^2-x+1>x^2-x+1/3-x+1/4

<-->6x^2+12x+48-2x^2+2x-2>4x^2-4x+4-3x-3(bo mau)

<--->6x^2+12x-2x^2+2x-4x^2+4x+3x>4-3+2-48

<--->21x>-45

--->x>-45/21=-15/7  mà x nguyên âm 

----->x \(\in\){-1;-2}

c)2(3-x)-1,5(x-4)<3-x

<--->6-2x-1,5x+6<3-x

<--->6+6-3<2x+1,5x-x

<--->9<2,5x

<--->3,6<x mà x la so nguyen nhỏ nhất 

--->x=4

\(\frac{2-x}{3}< \frac{3-2x}{5}+\frac{1}{3}\)

\(\Leftrightarrow5\left(2-x\right)< 3\left(3-2x\right)+5\)

\(\Leftrightarrow10-5x< 9-6x+5\)

\(\Leftrightarrow10-5x< -6x+14\)

\(\Leftrightarrow x< 4\)

Vậy bất phương trình có tập nghiệm là: S ={x| x < 4}

#Học tốt!

\(\frac{x+4}{5}+\frac{3x+2}{10}< \frac{x-1}{3}\)

\(\Leftrightarrow\frac{6\left(x+4\right)}{30}+\frac{3\left(3x+2\right)}{30}< \frac{10\left(x-1\right)}{30}\)

\(\Leftrightarrow6x+24+9x+6< 10x-10\)

\(\Leftrightarrow5x+40< 0\)

\(\Leftrightarrow x< -8\)

Tự biểu diễn nha bạn

\(\frac{x+4}{5}+\frac{3x+2}{10}< \frac{x-1}{3}\)

\(\Rightarrow\frac{6\left(x+4\right)}{30}+\frac{3\left(3x+2\right)}{30}< \frac{10\left(x-1\right)}{30}\)

\(\Rightarrow6x+24+9x+6< 10x-10\)

\(5x< -40\)

\(\Rightarrow x< -8\)

\(\frac{x+4}{5}+\frac{3x+2}{10}< \frac{x-1}{3}\)

\(\Leftrightarrow\frac{4\left(x+4\right)}{30}+\frac{3\left(3x+2\right)}{30}< \frac{10\left(x-1\right)}{30}\)

\(\Leftrightarrow\frac{4x+16+9x+6}{30}< \frac{10x-10}{30}\)

\(\Leftrightarrow\frac{13x+22}{30}< \frac{10x-10}{30}\)

\(\Leftrightarrow13x+22< 10x-10\)

\(\Leftrightarrow13x-10x< -22-10\)

\(\Leftrightarrow3x< -33\)

\(\Leftrightarrow x< -11\)

Kl : BPT có nghiệm { x/ x<-11}

Bn tự biểu diễn nhé ! 

Xin phép bỏ biểu diễn trên trục :))

a) \(2x-1< 2\left(x-1\right)\)

\(\Leftrightarrow2x-1< 2x-2\)

\(\Leftrightarrow2x-2x< 1-2\)

\(0x< -1\)( vô lí )

Vậy bất phương trình vô nghiệm.

b) \(\frac{x-1}{3}-\frac{2+3x}{4}>\frac{1}{6}\)

\(\Leftrightarrow\frac{4\left(x-1\right)-3\left(2+3x\right)}{12}>\frac{2}{12}\)

\(\Leftrightarrow4x-4-6-9x>2\)

\(\Leftrightarrow-5x-10>2\)

\(\Leftrightarrow-5x>12\)

\(\Leftrightarrow x< \frac{-12}{5}\)

Vậy...........