1) \(x^{15}=x\Leftrightarrow\hept{\begin{cases}x=0\\x=1\end{cases}}\)

a. (3x-1)⁵=32                b. (9x-1)²=(2x-3)²

=>(3x-1)⁵=2³                       =>9x-1=2x-3

=>3x-1=2                      =>9x-1-2x+3=0

=>3x=3                         =>7x+2=0

=>x=1                           =>7x=-2 

                                    =>x=-2/7

a) \(x^2-5=0\)

\(\Leftrightarrow x^2=5\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=5\\x=-5\end{array}\right.\)

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

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

\(\Leftrightarrow5x\left(-x-2\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\-x-2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=-2\end{array}\right.\)

c) \(\frac{4}{9}\cdot x^2=-4x-9\)

\(\Leftrightarrow\left(\frac{2}{3}x\right)^2+4x+9=0\)

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

\(\Leftrightarrow\)\(\frac{2}{3}x+3=0\Leftrightarrow x=-\frac{9}{2}\)

Tìm x

a, 5x - 10 . (-7) = 15 . (-3)

5x + 70 = -45

5x = -45 - 70

5x = -115

x = -115 : 5

x = -23

Vậy x = -23.

b, 2x + 12 = -8

2x = -8 - 12

2x = -20

x = -20 : 2

x = -10

Vậy x = -10.

c, 3x - 5 = -20

3x = -20 + 5

3x = -15

x = -15 : 3

x = -5

Vậy x = -5.

d, 2x - (-12) = -8 . 23

2x + 12 = -184

2x = -184 - 12

2x = -196

x = -196 : 2

x = -98

Vậy x = -98.

e, x² = 49

x² = 7² = (-7)²

=> x = 7 hoặc x = -7.

Vậy x thuộc {-7 ; 7}

i, (x - 2)² + 1 = 65

(x - 2)² = 65 - 1

(x - 2)² = 64

(x - 2)² = 8² = (-8)²

=> x - 2 = 8 hoặc x - 2 = -8

=> x = 10 hoăc x = -6

Vậy x thuộc {-6 ; 10}.

g, 2 (x - 3)² - 5 = 5 . (-3)²

2 (x - 3)² - 5 = 5 . 9

2 (x - 3)² - 5 = 45

2 (x - 3)² = 45 + 5

2 (x - 3)² = 50

(x - 3)² = 50 : 2

(x - 3)² = 25

(x - 3)² = 5² = (-5)²

=> x - 3 = 5 hoặc x - 3 = -5

=> x = 8 hoặc x = -2

Vậy x thuộc {-2 ; 8}.

a) 5x - 10.(-7)=15.(-3)      b) 2x+12=-8     c) 3x-5=-20        d)2x-(-12)=-8.23      e)\(^{x^2}\)=49      i)\(\left(x-2\right)^2+1\)=65

 5x+70=-45                          2x=-8-12           3x=-20+5           2x+12=-184                 x=7            \(\left(x-2\right)^2\) =64

5x=-45-70                            2x=-20               3x=-15              2x=-184-12                                      X-2            =8

5x=-115                                 x=-20:2             x=-15:3            2x=-186                                             x                =10

x=-23                                      x=-10                x=-5                   x=-93

g)\(2.\left(x-3\right)^2-5=5.\left(-3\right)^2\)

   \(2\left(x-3\right)^2-5=30\)

 \(2.\left(x-3\right)^2=35\)

\(2.\left(x^2-2x.3+3^2\right)=35\)

\(2x^2-24x+18=35\)

\(2x^2-24x=17\)

\(2x\left(x-12\right)=17\)

\(\orbr{\begin{cases}2x=17\\x-12=17\end{cases}}\orbr{\begin{cases}x=\frac{17}{2}\\x=29\end{cases}}\)

lộghjhkjkfnnkl

\(a,\left(\dfrac{2}{3}\right)^x=\left(\dfrac{4}{9}\right)^4.\)

\(\left(\dfrac{2}{3}\right)^x=\left[\left(\dfrac{2}{3}\right)^2\right]^4.\)

\(\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^8\Rightarrow x=8.\)

Vậy.....

\(b,\left(2x-1\right)^2=25.\)

\(\left(2x-1\right)^2=\left(\pm5\right)^2.\)

\(\Rightarrow\left(2x-1\right)=\pm5.\)

+) Xét \(2x-1=5\), ta có:

\(2x-1=5.\)

\(\Rightarrow2x=6.\)

\(\Rightarrow x=3.\)

+) Xét \(2x-1=-5\), ta có:

\(2x-1=-5.\)

\(\Rightarrow2x=-4.\)

\(\Rightarrow x=-2.\)

Vậy.....