a, \(\sqrt{2x^2-3}=\sqrt{4x-3}\) (x \(\ge\) \(\sqrt{\dfrac{3}{2}}\))

Vì hai vế ko âm, bp 2 vế ta được:

2x² - 3 = 4x - 3

\(\Leftrightarrow\) 2x² = 4x

\(\Leftrightarrow\) x² = 2x

\(\Leftrightarrow\) x² - 2x = 0

\(\Leftrightarrow\) x(x - 2) = 0

\(\Leftrightarrow\) \(\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(KTM\right)\\x=2\left(TM\right)\end{matrix}\right.\)

Vậy S = {2}

b, \(\sqrt{2x-1}=\sqrt{x-1}\) (x \(\ge\) 1)

Vì hai vế ko âm, bp 2 vế ta được:

2x - 1 = x - 1

\(\Leftrightarrow\) x = 0 (KTM)

Vậy x = \(\varnothing\)

c, \(\sqrt{x^2-x-6}=\sqrt{x-3}\) (x \(\ge\) 3)

Vì hai vế ko âm, bp 2 vế ta được:

x² - x - 6 = x - 3

\(\Leftrightarrow\) x² - 2x - 3 = 0

\(\Leftrightarrow\) x² - 3x + x - 3 = 0

\(\Leftrightarrow\) x(x - 3) + (x - 3) = 0

\(\Leftrightarrow\) (x - 3)(x + 1) = 0

\(\Leftrightarrow\) \(\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(TM\right)\\x=-1\left(KTM\right)\end{matrix}\right.\)

Vậy S = {3}

d, \(\sqrt{x^2-x}=\sqrt{3x-5}\) (x \(\ge\) \(\dfrac{5}{3}\))

Vì hai vế ko âm, bp 2 vế ta được:

x² - x = 3x - 5

\(\Leftrightarrow\) x² - 4x + 5 = 0

\(\Leftrightarrow\) x² - 4x + 4 + 1 = 0

\(\Leftrightarrow\) (x - 2)² + 1 = 0

Vì (x - 2)² \(\ge\) 0 với mọi x \(\ge\) \(\dfrac{5}{3}\) \(\Rightarrow\) (x - 2)² + 1 > 0 với mọi x \(\ge\) \(\dfrac{5}{3}\)

\(\Rightarrow\) Pt vô nghiệm

Vậy S = \(\varnothing\)

Chúc bn học tốt!

Nguyễn Lê Phước Thịnh nhờ anh xíu ạ

a: =>2x-3x^2-x<15-3x^2-6x

=>x<-6x+15

=>7x<15

=>x<15/7

b: =>4x^2-24x+36-4x^2+4x-1>=12x

=>-20x+35>=12x

=>-32x>=-35

=>x<=35/32

\(a,2x-x\left(3x+1\right)< 15-3x\left(x+2\right)\\ \Leftrightarrow2x-3x^2-x< 15-3x^2-6x\\ \Leftrightarrow3x^2-3x^2+2x+6x-x< 15\\ \Leftrightarrow7x< 15\\ \Leftrightarrow x< \dfrac{15}{7}\)

Vậy S={-∞; 15/7}

\(b,4\left(x-3\right)^2-\left(2x-1\right)^2\ge12x\\ \Leftrightarrow4\left(x^2-6x+9\right)-\left(4x^2-4x+1\right)-12x\ge0\\ \Leftrightarrow4x^2-4x^2-24x+4x-12x\ge-36+1\\ \Leftrightarrow-32x\ge-35\\ \Leftrightarrow x\le\dfrac{35}{32}\)

Vậy S={-∞; 35/32]

a, \(5\left|2x-1\right|-3=7\Leftrightarrow5\left|2x-1\right|=10\Leftrightarrow\left|2x-1\right|=2\)

TH1 : \(2x-1=2\Leftrightarrow x=\frac{3}{2}\)

TH2 : \(2x-1=-2\Leftrightarrow x=-\frac{1}{2}\)

b, \(\left(2x+3\right)\left(x-2\right)-x^2+4=0\Leftrightarrow\left(2x+3\right)\left(x-2\right)-\left(x-2\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(2x+3-x-2\right)=0\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\Leftrightarrow x=-1;x=2\)

c, \(\frac{2x-3}{2}< \frac{1-3x}{-5}\Leftrightarrow\frac{2x-3}{2}+\frac{1-3x}{5}< 0\)

\(\Leftrightarrow\frac{10x-15+2-6x}{10}< 0\Rightarrow4x-13< 0\Leftrightarrow x< \frac{13}{4}\)

\(a,\dfrac{2x-1}{3}< \dfrac{x+6}{2}\)

\(\Leftrightarrow\dfrac{4x-2}{6}< \dfrac{3x+18}{6}\)

\(\Leftrightarrow4x-2< 3x+18\)

\(\Leftrightarrow4x-3x< 2+18\)

\(\Leftrightarrow x< 20\)

\(b,\dfrac{5\left(x-1\right)}{6}-1>\dfrac{2\left(x+1\right)}{3}\)

\(\Leftrightarrow\dfrac{5x-11}{6}>\dfrac{4x+4}{6}\)

\(\Leftrightarrow5x-11>4x+4\)

\(\Leftrightarrow5x-4x>11+4\)

\(\Leftrightarrow x>15\)

a,\(Đkxđ:\hept{\begin{cases}x\ne0\\x\ne2\end{cases}}\) 

 \(=\frac{x+2}{x-2}+\frac{2}{x^2-2x}+\frac{1}{x}\)

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

\(=\frac{x\left(x+2\right)+2+x-2}{x\left(x-2\right)}\)

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

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

\(\Rightarrow\frac{x+3}{x-2}=0\Leftrightarrow x+3=0\Rightarrow x=-3\left(tm\right)\)

b, \(\left(x-3\right)\left(2x+1\right)=\left(x-3\right)\left(x-1\right)\)

\(\Rightarrow\left(x-3\right)\left(2x+1\right)-\left(x-3\right)\left(x-1\right)=0\)

\(\Rightarrow\left(x-3\right)\left(2x+1-x+1\right)=0\)

\(\Rightarrow\left(x-3\right)\left(x+2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}\)

c, \(|x-5|=2x+1\)

\(\Rightarrow|x-5|=\orbr{\begin{cases}x-5\Leftrightarrow x-5\ge0\Rightarrow x\ge5\\x-5\Leftrightarrow x-5< 0\Rightarrow x< 5\end{cases}}\)

Nếu \(x\ge5\Rightarrow x-5=2x+1\)

\(\Rightarrow x=-6\left(ktm\right)\)

Nếu \(x< 5\Rightarrow-\left(x-5\right)=2x+1\)

\(\Rightarrow-x+5=2x+1\)

\(\Rightarrow3x=4\)

\(\Rightarrow x=\frac{4}{3}\left(tm\right)\)

Vậy \(S=\left\{\frac{4}{3}\right\}\)

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

\(\left(3x+1\right)\left(x-5\right)\left(-4x+5\right)\ge0\Leftrightarrow\left[{}\begin{matrix}x\le-\frac{1}{3}\\\frac{5}{4}\le x\le5\end{matrix}\right.\)

\(\frac{x+2}{x-2}\le\frac{3x+1}{2x-1}\Leftrightarrow\frac{3x+1}{2x-1}-\frac{x+2}{x-2}\ge0\)

\(\Leftrightarrow\frac{x^2-8x}{\left(2x-1\right)\left(x-2\right)}\ge0\Leftrightarrow\frac{x\left(x-8\right)}{\left(2x-1\right)\left(x-2\right)}\ge0\Leftrightarrow\left[{}\begin{matrix}x\le0\\\frac{1}{2}< x< 2\\x\ge8\end{matrix}\right.\)

bai 1

1 thay k=0 vao pt ta co 4x^2-25+0^2+4*0*x=0

<=>(2x)^2-5^2=0

<=>(2x+5)*(2x-5)=0

<=>2x+5=0 hoăc 2x-5 =0 tiếp tục giải ý 2 tương tự

3:

Gọi hai số cần tìm lần lượt là a,b

Theo đề, ta có: a=2b và a-b=22

=>b=22; a=44