\(\Rightarrow\left(3x-1\right)^{20}-\left(3x-1\right)^{10}=0\\ \Rightarrow\left(3x-1\right)^{10}\left[\left(3x-1\right)^{10}-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}3x-1=0\\\left(3x-1\right)^{10}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x-1=0\\3x-1=1\\3x-1=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=\dfrac{2}{3}\\x=0\end{matrix}\right.\)

Đề bài yêu cầu tìm gì thế?

\(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\)

\(\Rightarrow\left(3x-1\right)^{10}=\left(3x-1\right)^{20}=0\)

\(\Rightarrow\left(3x-1\right)^{10}.\left[\left(3x-1\right)^{10}-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\\left(3x-1\right)^{10}-1=0\end{cases}\Rightarrow\orbr{\begin{cases}3x-1=0\\3x-1=\pm0\end{cases}}}\)

\(\left(+\right)3x-1=0\Rightarrow x=\frac{1}{3}\)

\(\left(+\right)\orbr{\begin{cases}3x-1=1\\2x-1=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=0\end{cases}}}\)

\(\Rightarrow x\in\left\{\frac{1}{3};\frac{2}{3};0\right\}\)

a ) 10 x X - 1 - 3 - 5 - 7 - ... - 19 = 2 + 4 + 6 + ... + 20

10 x X - 1 - 3 - 5 - 7 - ... - 19 = 110

10 x X - ( 1 + 3 + 5 + 7 + ... + 19 ) = 110

10 x X - 100 = 110

10 x X = 110 + 100

10 x X = 210

       X = 210 : 10

       X = 21

a 10 x X-1-3-5-7-....-19 = 2+4+6+....+20

​10xX-1-3-5-7-....-19=110

​10xX=110+1+3+5+7+....+19

​10xX=210

​X=210:10

​X=21

b là 4

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mong các bạn giúp tớ sáng mai phải đi học rùi huhuhu

a) \(\left(3x-2\right)\left(3x+2\right)-\left(3x+4\right)^2=20\\ \Rightarrow9x^2-4-9x^2-24x-16-20=0\\ \Rightarrow-24x-40=0\\ \Rightarrow-24x=40\\ \Rightarrow x=-\dfrac{5}{3}\)

b) \(6x^2-2x\left(3x+1\right)=10\\ \Rightarrow6x^2-6x^2-2x=10\\ \Rightarrow-2x=10\\ \Rightarrow x=-5\)

c) \(x^2+4x+3=0\\ \Rightarrow\left(x+1\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\x+3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)

\(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\)

\(\Rightarrow\left(3x-1\right)^{20}-\left(3x-1\right)^{10}=0\)

\(\Rightarrow\left(3x-1\right)^{10}\left[\left(3x-1\right)^2-1\right]=0\)

\(\Rightarrow\left(3x-1\right)^{10}\left(3x-1+1\right)\left(3x-1-1\right)=0\)

\(\Rightarrow\left(3x-1\right)^{10}.3x.\left(3x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}3x=0\\3x-1=0\\3x-2=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\3x=1\\3x=2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=\dfrac{2}{3}\end{matrix}\right.\)

x = 0 hoặc 1/3 hoặc 2/3

(3x - 1)¹⁰ = (3x - 1)²⁰

(3x - 1)²⁰ - (3x - 1)¹⁰ = 0

(3x - 1)¹⁰ . (3x - 1)¹⁰ - (3x - 1)¹⁰ . 1 = 0

(3x - 1)¹⁰ . [(3x - 1)¹⁰ - 1] = 0

\(\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\\left(3x-1\right)^{10}-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}3x-1=0\\\left(3x-1\right)^{10}=1\end{cases}}\)

3x - 1 = 0                                 (3x - 1)¹⁰ = 1

=> 3x = 1                                 3x - 1 = 1    hoặc    3x - 1 = -1    

=> x = \(\frac{1}{3}\)                               3x = 2         hoặc     3x = 0

                                               x = \(\frac{2}{3}\)        hoặc    x = 0     

(3x-1)¹⁰là dương mà

\(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\)

\(\Rightarrow\left(3x-1\right)^{20}-\left(3x-1\right)^{10}=0\)

\(\left(3x-1\right)^{10}.\left[\left(3x-1\right)^{10}-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\\left(3x-1\right)^{10}-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}3x-1=0\\3x-1^{10}=1\end{cases}}}\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=\frac{2}{3}ho\text{ặc}x=0\end{cases}}\)

Vậy \(x=\frac{1}{3}ho\text{ặc}x=\frac{2}{3}ho\text{ặc}x=0\)

Tham khảo nhé~

TA CÓ:\(\left(3x-1\right)^{10}-\left(3x-1\right)^{20}=0\)

\(\Rightarrow\left(3x-1\right)^{10}-\left(3x-1\right)^{10}\times\left(3x-1\right)^{10}=0\)

\(\Rightarrow\left(3x-1\right)^{10}\times[1-\left(3x-1\right)^{10}]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\1-\left(3x-1\right)^{10}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=\frac{2}{3}\end{cases}}}\)

mik nha. cảm ơn nhìu!! ^^

\(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\)

\(\Rightarrow\left(3x-1\right)^{10}-\left(3x-1\right)^{20}=0\)

\(\Rightarrow\left(3x-1\right)^{10}\left[1-\left(3x-1\right)^{10}\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\1-\left(3x-1\right)^{10}=0\end{cases}}\Rightarrow\orbr{\begin{cases}\left(3x-1\right)^{10}=0\\\left(3x-1\right)^{10}=1\end{cases}}\)

TH 1 : \(\left(3x-1\right)^{10}=0\Rightarrow3x-1=0\Rightarrow3x=1\Rightarrow x=\frac{1}{3}\)

TH 2 : \(\left(3x-1\right)^{10}=1\Rightarrow\orbr{\begin{cases}3x-1=1\\3x-1=-1\end{cases}}\Rightarrow\orbr{\begin{cases}3x=2\\3x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=0\end{cases}}\)

Vậy  \(x\in\left\{\frac{1}{3};\frac{2}{3};0\right\}\)

_Chúc bạn học tốt_

10.(3x-1)=20

(3x-1)=20:10

3x-1=2

3x=2+1

3x=3

x=3:3

x=1

10 . ( 3 x - 1 ) = 20

          3 x - 1   = 20 : 10

          3 x - 1   = 2

                3 x   = 2 - 1

                 3 x  = 1

                    x   = 1 : 3 = 1/3

10 . (3x - 1 ) = 20

        3x-1      = 20 : 10

         3x-1      = 2

         3x          = 2 + 1

         3x           = 3

           x           = 3 : 3

           x            = 1