a: =>4(2x-1)-12x=3(x+3)+24

=>8x-4-12x=3x+9+24

=>-4x-4=3x+33

=>-7x=37

=>x=-37/7

b: =>(x-2)(x+2+x-9)=0

=>(2x-7)(x-2)=0

=>x=2 hoặc x=7/2

c: =>(x-1)(x+3)-x+3=3x+3

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

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

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

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

=>x=-1

ĐKXĐ:\(x\ne\pm1\)

\(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}+\dfrac{x^2+3x-2}{1-x^2}=0\\ \Leftrightarrow\dfrac{\left(x+1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{x^2+3x-2}{\left(x+1\right)\left(x-1\right)}=0\\ \Leftrightarrow\dfrac{x^2+2x+1-x^2+2x-1-x^2-3x+2}{\left(x+1\right)\left(x-1\right)}=0\\ \Rightarrow-x^2+x+2=0\\ \Leftrightarrow x^2-x-2=0\\ \Leftrightarrow\left(x^2-2x\right)+\left(x-2\right)=0\\ \Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)

\(ĐK:x\ne\pm1\)

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

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

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

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(ktm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)

\(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}+\dfrac{x^2+3x-2}{1-x^2}=0\left(ĐKXĐ:x\ne\pm1\right)\)

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

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

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

\(\Leftrightarrow x^2-x-2=0\)

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

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

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

\(\Leftrightarrow x=2\) (nhận) hay \(x=-1\) (loại).

-Vậy \(S=\left\{2\right\}\)

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E mới lớp 7 chị ơi

Bài làm:

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

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

=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\) hoặc \(\orbr{\begin{cases}x=-1\\x=-2\end{cases}}\)

Vậy tập nghiệm PT \(S=\left\{-2;-1;0;1\right\}\)

b) Nhận thấy \(\left(x-1\right)^4+\left(x-2\right)^4=0\)

\(\Leftrightarrow\left(x-1\right)^4=-\left(x-2\right)^4\)

Mà \(\hept{\begin{cases}\left(x-1\right)^4\ge0\\-\left(x-2\right)^4\le0\end{cases}\left(\forall x\right)}\) 

Dấu "=" xảy ra khi: \(\hept{\begin{cases}\left(x-1\right)^4=0\\-\left(x-2\right)^4=0\end{cases}}\Rightarrow\hept{\begin{cases}x=1\\x=2\end{cases}}\) (vô lý)

=> không tồn tại x thỏa mãn PT

a) x( x - 1 )( x + 1 )( x + 2 ) = 0

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

<=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\), \(\orbr{\begin{cases}x=-1\\x=-2\end{cases}}\)

b) ( x - 1 )⁴ + ( x - 2 )⁴ = 0

<=> ( x - 1 )⁴ = -( x - 2 )⁴

\(\hept{\begin{cases}\left(x-1\right)^4\ge0\\-\left(x-2\right)^4\le0\end{cases}\forall}x\)

Đẳng thức xảy ra <=> \(\hept{\begin{cases}x-1=0\\x-2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\x=2\end{cases}}\)( mâu thuẫn )

=> Phương trình vô nghiệm

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

\(\Leftrightarrow\hept{\begin{cases}x-1=0\\x+1=0\\x+2=0\end{cases};x=0}\Leftrightarrow\hept{\begin{cases}x=1\\x=-1\\x=-2\end{cases};x=0}\)

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

Ta có  : \(\left(x-1\right)^4\ge0;\left(x-2\right)^4\ge0\)

\(< =>\left(x-1\right)^4+\left(x-2\right)^4\ge0\)

Dấu = xảy ra khi \(< =>\hept{\begin{cases}x=1\\x=2\end{cases}}\)(vô lý)

\(\frac{x-1}{2018}+\frac{x-2}{2017}+\frac{x-3}{2016}+\frac{x-2043}{8}\)\(=0\)

\(\Leftrightarrow\)\(\frac{x-1}{2018}-1+\frac{x-2}{2017}-1+\frac{x-3}{2016}-1\)\(+\frac{x-2043}{8}+3=0\)

\(\Leftrightarrow\)\(\frac{x-1}{2018}-\frac{2018}{2018}+\frac{x-2}{2017}-\frac{2017}{2017}\)\(+\frac{x-3}{2016}-\frac{2016}{2016}+\frac{x-2043}{8}+\frac{24}{8}=0\)

\(\Leftrightarrow\)\(\frac{x-2019}{2018}+\frac{x-2019}{2017}+\frac{x-2019}{2016}\)\(+\frac{x-2019}{8}=0\)

\(\Leftrightarrow\)\(\left(x-2019\right).\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\right)=0\)

\(\Leftrightarrow\)\(x-2019=0\) ( Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\ne0\))

\(\Leftrightarrow\) \(x=2019\)

Vậy phương trình có nghiệm là : \(x=2019\)