roois vãi

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rối thế bn

a,\(2x+5=2-x\)

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

\(< =>3x+3=0\)

\(< =>x=-1\)

b, \(/x-7/=2x+3\)

Với \(x\ge7\)thì \(PT< =>x-7=2x+3\)

\(< =>2x-x+3+7=0\)

\(< =>x+10=0< =>x=-10\)( lọai )

Với \(x< 7\)thì \(PT< =>7-x=2x+3\)

\(< =>2x+x+3-7=0\)

\(< =>3x-4=0< =>x=\frac{4}{3}\) ( loại )

c,\(\frac{4}{x+2}-\frac{4x-6}{4x-x^3}=\frac{x-3}{x\left(x-2\right)}\left(đk:x\ne-2;0;2\right)\)

\(< =>\frac{4x\left(x-2\right)}{x\left(x-2\right)\left(x+2\right)}+\frac{4x-6}{x\left(x-2\right)\left(2+x\right)}=\frac{\left(x-3\right)\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}\)

\(< =>4x^2-8x+4x-6=x^2-x-6\)

\(< =>4x^2-x^2-4x+x-6+6=0\)

\(< =>3x^2-3x=0< =>3x\left(x-1\right)=0< =>\orbr{\begin{cases}x=0\left(loai\right)\\x=1\left(tm\right)\end{cases}}\)

c) \(\dfrac{x}{x-2}+\dfrac{x}{x+2}=\dfrac{4x}{x^2-4}.ĐKXĐ:x\ne2;-2\)

<=>\(\dfrac{x\left(x+2\right)}{x^2-4}+\dfrac{x\left(x-2\right)}{x^2-4}=\dfrac{4x}{x^2-4}\)

<=>x²+2x+x²-2x=4x

<=>2x²-4x=0

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

<=>\(\left[{}\begin{matrix}2x=0< =>x=0\\x-2=0< =>x=2\left(loại\right)\end{matrix}\right.\)

Vậy pt trên có nghiệm là S={0}

d) 11x-9=5x+3

<=>11x-5x=9+3

<=>6x=12

<=>x=2

Vậy pt trên có nghiệm là S={2}

e) (2x+3)(3x-4) =0

<=> \(\left[{}\begin{matrix}2x+3=0< =>x=\dfrac{-3}{2}\\3x-4=0< =>x=\dfrac{4}{3}\end{matrix}\right.\)

Vậy pt trên có tập nghiệm là S={\(\dfrac{-3}{2};\dfrac{4}{3}\)}

a) 5x+9 =2x

<=> 5x-2x=9

<=> 3x=9

<=> x=3

Vậy pt trên có nghiệm là S={3}

b) (x+1)(4x-3)=(2x+5)(x+1)

<=> (x+1)(4x-3)-(2x+5)(x+1)=0

<=>(x+1)(2x-8)=0

<=>\(\left[{}\begin{matrix}x+1=0< =>x=-1\\2x-8=0< =>2x=8< =>x=4\end{matrix}\right.\)

Vậy pt trên có tập nghiệm là S={-1;4}

c) 

<=>

<=>x²+2x+x²-2x=4x

<=>2x²-4x=0

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

<=>

Vậy pt trên có nghiệm là S={0}

d) 11x-9=5x+3

<=>11x-5x=9+3

<=>6x=12

<=>x=2

Vậy pt trên có nghiệm là S={2}

e) (2x+3)(3x-4) =0

<=> 

Vậy pt trên có tập nghiệm là S={}

a) Ta có: \(3x-1=0\)

\(\Leftrightarrow3x=1\)

\(\Leftrightarrow x=\dfrac{1}{3}\)

Vậy: \(S=\left\{\dfrac{1}{3}\right\}\)

b) Ta có: \(5x-2=x+4\)

\(\Leftrightarrow5x-x=4+2\)

\(\Leftrightarrow4x=6\)

\(\Leftrightarrow x=\dfrac{3}{2}\)

Vậy: \(S=\left\{\dfrac{3}{2}\right\}\)

\(a,PT\Leftrightarrow\left|x+3\right|=3x-6\\ \Leftrightarrow\left[{}\begin{matrix}x+3=3x-6\left(x\ge-3\right)\\x+3=6-3x\left(x< -3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\left(tm\right)\\x=\dfrac{3}{4}\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow x=\dfrac{9}{2}\\ b,PT\Leftrightarrow\left|x-1\right|=\left|2x-1\right|\\ \Leftrightarrow\left[{}\begin{matrix}x-1=2x-1\\1-x=2x-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)

\(c,ĐK:x\le\dfrac{2}{5}\\ PT\Leftrightarrow4-5x=25x^2-20x+4\\ \Leftrightarrow25x^2-15x=0\\ \Leftrightarrow5x\left(5x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=\dfrac{3}{5}\left(ktm\right)\end{matrix}\right.\Leftrightarrow x=0\\ d,ĐK:x\le\dfrac{2}{5}\\ PT\Leftrightarrow4-5x=2-5x\\ \Leftrightarrow x\in\varnothing\)

\(\frac{x^2-4x+1}{x+1}+2=-\frac{x^2-5x+1}{2x+1}\):

\(ĐKXĐ:x\ne-1;x\ne-\frac{1}{2}\)

PT \(\Leftrightarrow\frac{x^2-4x+1}{x+1}+1+\frac{x^2-5x+1}{2x+1}+1=0\)

         \(\Leftrightarrow\frac{x^2-3x+2}{x+1}+\frac{x^2-3x+2}{x+1}=0\)

\(\Leftrightarrow\left(x^2-3x+2\right)\left(\frac{1}{x+1}+\frac{1}{2x+1}\right)=0\)

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

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

Cả 3 giá trị trên đều thỏa mãn ĐKXĐ

Vậy PT đã cho có tập nghiêm : \(S=\left\{1;2;-\frac{2}{3}\right\}\)

Chúc bạn học tốt !!!

3: =>x+3>=0 và x-2<=0

=>-3<=x<=2

4: =>4x^2-4x+3x-3<x^2-2x+1

=>3x^2+x-2<0

=>3x^2+3x-2x-2<0

=>(x+1)(3x-2)<0

=>-1<x<2/3

2: =>x^4-8x>0

=>x(x^3-8)>0

=>x>2 hoặc x<0

a. ĐKXĐ: \(x\ge\dfrac{1}{2}\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x^2+2x}=a>0\\\sqrt{2x-1}=b\ge0\end{matrix}\right.\)

\(\Rightarrow a+b=\sqrt{3a^2-b^2}\)

\(\Leftrightarrow\left(a+b\right)^2=3a^2-b^2\)

\(\Leftrightarrow a^2-ab-b^2=0\Leftrightarrow\left(a-\dfrac{1+\sqrt{5}}{2}b\right)\left(a+\dfrac{\sqrt{5}-1}{2}b\right)=0\)

\(\Leftrightarrow a=\dfrac{1+\sqrt{5}}{2}b\Leftrightarrow\sqrt{x^2+2x}=\dfrac{1+\sqrt{5}}{2}\sqrt{2x-1}\)

\(\Leftrightarrow x^2+2x=\dfrac{3+\sqrt{5}}{2}\left(2x-1\right)\)

\(\Leftrightarrow x^2-\left(\sqrt{5}+1\right)x+\dfrac{3+\sqrt{5}}{2}=0\)

\(\Leftrightarrow\left(x-\dfrac{\sqrt{5}+1}{2}\right)^2=0\)

\(\Leftrightarrow x=\dfrac{\sqrt{5}+1}{2}\)

b. ĐKXĐ: \(x\ge5\)

\(\Leftrightarrow\sqrt{5x^2+14x+9}=\sqrt{x^2-x-20}+5\sqrt{x+1}\)

\(\Leftrightarrow5x^2+14x+9=x^2-x-20+25\left(x+1\right)+10\sqrt{\left(x+1\right)\left(x-5\right)\left(x+4\right)}\)

\(\Leftrightarrow2x^2-5x+2=5\sqrt{\left(x^2-4x-5\right)\left(x+4\right)}\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x^2-4x-5}=a\ge0\\\sqrt{x+4}=b>0\end{matrix}\right.\)

\(\Rightarrow2a^2+3b^2=5ab\)

\(\Leftrightarrow\left(a-b\right)\left(2a-3b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^2-4x-5}=\sqrt{x+4}\\2\sqrt{x^2-4x-5}=3\sqrt{x+4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-4x-5=x+4\\4\left(x^2-4x-5\right)=9\left(x+4\right)\end{matrix}\right.\)

\(\Leftrightarrow...\)