\(x^6-7x^3-8=0\)

\(\Leftrightarrow\left(x^3+1\right)\left(x^3-8\right)=0\)

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

Ta có: \(x^2-x+1=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>0\)(loại)

\(x^2+2x+4=\left(x+1\right)^2+3>0\)(loại)

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

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-1\\x=2\end{array}\right.\)(thỏa mãn)

Vậy phương trình đã cho có tập nghiệm là S={-1;2}

biết gì???

Bạn hãy ra thêm đề nhé

(x³ - 4x² - 3x² + 12x + 2x - 8 =0
 x²(x - 4) - 3x(x - 4) + 2(x - 4) =0
 (x - 4)(x² - 3x + 2) =0
 (x - 4)(x - 1)(x - 2) =0

=>X-4=0       hoặc            x-1=0                       hoặc              x-2=0

(tự giải tiếp nhá)        

a)\(-2\left(x+6\right)+6\left(x-10\right)=8.\)

\(\Leftrightarrow-2x-12+6x-60=8\)

\(\Leftrightarrow4x=80\)

\(\Rightarrow x=20\)

b/ \(-4\left(2x+9\right)-\left(-8x+3\right)-\left(x+13\right)=0\)

\(\Leftrightarrow-8x-36+8x-3-x-13=0\)

\(\Leftrightarrow-x=52\)

\(\Rightarrow x=-52\)

c/\(7x\left(2+x\right)-7x\left(x+3\right)=14\)

\(\Leftrightarrow14x+7x^2-7x^2-21x=14\)

\(\Leftrightarrow-7x=14\)

\(\Rightarrow x=-2\)

minh cma on nha

b) -4.(2x+9)-(-8x+3)-(x+13)=0

a, - 2 .( x + 6 ) + 6 . ( x - 10 ) = 8

                - 2x - 12 + 6x - 60 = 8

                                4x - 72 = 8

                                       4x = 8 + 72

                                       4x = 80

                                         x = 20

b, - 4 . ( 2x + 9 ) - ( - 8x + 3 ) - ( x + 13 ) = 0

                       - 8x - 36 + 8x - 3 - x - 13 = 0

                                                - x - 52 = 0

                                                         x = - 52

c,  7x . ( 2 + x ) - 7x . ( x + 3 ) = 14

                7x . ( 2 + x - x - 3 ) = 14

                              7x . ( - 1 ) = 14 

                                         7x = 14 : ( - 1 )

                                         7x = - 14 

                                           x = - 2

d, 2 . ( 5 + 3x ) + x = 31

           10 + 6x + x = 31

                 10 + 7x = 31

                         7x = 31 - 10

                          7x = 21

                            x = 3

a)-2(x+6)+6(x-10)=8

-2x+-12+6x+-60=8

4x+-72=8

4x=80

x=80:4

x=20

b)-4(2x+9)-(-8x+3)-(x+13)=0

-8x+-36+8x-3+x-13=0

(-8x+8x)+-36+-3+x-13=0

0+-52+x=0

x=0-(-52)

x=-52

c)7x(2+x)-7x(x+3)=14

14x+7x²

|5\(x\) - 4| = |\(x+2\)|

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

\(\left[{}\begin{matrix}4x=6\\6x=2\end{matrix}\right.\)

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

vậy \(x\in\) { \(\dfrac{1}{3};\dfrac{3}{2}\)}

|2\(x\) - 3| - |3\(x\) + 2| = 0

|2\(x\) - 3| = | 3\(x\) + 2|

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

\(\left[{}\begin{matrix}x=-5\\x=\dfrac{1}{5}\end{matrix}\right.\)

vậy \(x\in\){ -5; \(\dfrac{1}{5}\)}

|\(\dfrac{5}{4}\)\(x\) - \(\dfrac{7}{2}\)| - | \(\dfrac{5}{8}\)\(x\) + \(\dfrac{3}{5}\)| = 0

|\(\dfrac{5}{4}x\) - \(\dfrac{7}{2}\)|    = | \(\dfrac{5}{8}x+\dfrac{3}{5}\)|

\(\left[{}\begin{matrix}\dfrac{5}{4}x-\dfrac{7}{2}=\dfrac{5}{8}x+\dfrac{3}{5}\\\dfrac{5}{4}x-\dfrac{7}{2}=-\dfrac{5}{8}x-\dfrac{3}{5}\end{matrix}\right.\)

  \(\left[{}\begin{matrix}\dfrac{5}{4}x-\dfrac{5}{8}x=\dfrac{3}{5}+\dfrac{7}{2}\\\dfrac{5}{4}x+\dfrac{5}{2}x=-\dfrac{3}{5}+\dfrac{7}{2}\end{matrix}\right.\)

 \(\left[{}\begin{matrix}\dfrac{5}{8}x=\dfrac{41}{10}\\\dfrac{15}{8}x=\dfrac{29}{10}\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=\dfrac{164}{25}\\x=\dfrac{116}{75}\end{matrix}\right.\)

Vậy \(x\in\) { \(\dfrac{116}{75}\); \(\dfrac{164}{25}\)}

\(a,\Leftrightarrow\left(4x-8\right)\left(x+1\right)=0\\ \Leftrightarrow4\left(x-2\right)\left(x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ b,\Leftrightarrow\left(x+1\right)\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2=-1\left(vô.lí\right)\end{matrix}\right.\Leftrightarrow x=-1\\ c,\Leftrightarrow x^2-2x-4x+8=0\\ \Leftrightarrow\left(x-2\right)\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\\ d,\Leftrightarrow x^3-3x^2+3x-9x+2x-6=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+x+2x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=-2\end{matrix}\right.\)

a) \(\Rightarrow4\left(x+1\right)\left(x-2\right)=0\)

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

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

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

\(\Rightarrow x=-1\left(do.x^2+1\ge1>0\right)\)

c) \(\Rightarrow x\left(x-4\right)-2\left(x-4\right)=0\)

\(\Rightarrow\left(x-4\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)

d) \(\Rightarrow x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)

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

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

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

   + -2X-12+6X-60=8

<=>4X=80]

<=> X = 20

         V.....

   + -8X-36 +8X -3 - X - 13 =0

 <=> -X = 52

 <=> X = -52

           V.....

   + 14X +7\(X^2\)-7\(X^2\)-21X=14

    <=> -7X  =14

     <=> X= -2 

              V .......