Mk cần gấp để nộp ạ

Bài 1: Tìm x , biết :

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

<x-1=0

|

<x=0+1=1

-<x-2=0

-<x=0+2=2

Vậy x E {1;2}

b) (x-2).(x^2+1)=0

[<x-2=0

[<x=0+2=2

[>x²+1=0

   x²=0-1

   x²=1.(-1)

c) (x+`1).(x^2-4)=0

Bài 4:

a: |x-2|=0

=>x-2=0

=>x=2

b: |x+3|=1

=>\(\left[\begin{array}{l}x+3=1\\ x+3=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1-3=-2\\ x=-1-3=-4\end{array}\right.\)

c: \(-3\left|4-x\right|=-9\)

=>|4-x|=3

=>|x-4|=3

=>\(\left[\begin{array}{l}x-4=3\\ x-4=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=7\\ x=1\end{array}\right.\)

d: |2x+1|=-2

mà -2<0<=|2x+1|

nên x∈∅

Bài 5:

a: \(\left(x+3\right)^2=36\)

=>\(\left[\begin{array}{l}x+3=6\\ x+3=-6\end{array}\right.\Rightarrow\left[\begin{array}{l}x=6-3=3\\ x=-6-3=-9\end{array}\right.\)

b: \(\left(x+5\right)^2=100\)

=>\(\left[\begin{array}{l}x+5=10\\ x+5=-10\end{array}\right.\Rightarrow\left[\begin{array}{l}x=10-5=5\\ x=-10-5=-15\end{array}\right.\)

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

=>2x-4=0

=>2x=4

=>x=2

d: \(\left(x-1\right)^3=27\)

=>x-1=3

=>x=4

Bài 1: Tính bằng 2 cách:

a) 2^5 : 2^4

= 2

b) 3^4 : 3^2

= 3

c) 6^3 : 6^2

= 6

d) 8^4 : 8^2

= 8^2

= 64

e) 7^5 : 7^4

= 7

f) 100^3 : 100

= 100^2

= 10000

Bài 2: Tìm số tự nhiên x, biết:

a) 2^x = 16

2^x = 2^4

x = 4

Vậy x = 4

b) 3^x = 243

3^x = 3^5

x = 5

Vậy x = 5

c) 5^x+1 = 125

5^x + 1 = 5^3

x + 1 = 3

x = 3 - 1

x = 2

Vậy x = 2

Bài 1 : x/3 = y/4 = z/5 => x²/9 = y²/16 = z²/25 
=> 2x²/18 = 2y²/32 = 3z²/75 
=> x²/9 = (2x² + 2y² - 3z²)/(18 + 32 - 75) = - 100/(-25) = 1/4 
=> x²/9 = 1/4 => x² = 9/4 => x = ±3/2 
y²/16 = 1/4 => y² = 4 => y = ± 2 
z²/25 = 1/4 => z² = 25/4 => z = ±5/2 
Mà x, y, z cùng dấu. 
Vậy (x ; y ; z) = (3/2 ; 2 ; 5/2) , (-3/2 ; -2 ; -5/2)

B3 ko tìm được x,y,z thỏa mãn do kết quả là 1 số không dương

a) \(\left(x+5\right)^2=100\Leftrightarrow\orbr{\begin{cases}\left(x+5\right)^2=10^2\\\left(x+5\right)^2=\left(-10\right)^2\end{cases}\Leftrightarrow\orbr{\begin{cases}x+5=10\\x+5=-10\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=5\\x=-15\end{cases}}}\)

b) \(\left(2x-4\right)^2=0\Leftrightarrow2x-4=0\Leftrightarrow2x=4\Leftrightarrow x=2\)

c) \(\left(x-1\right)^3=27\Leftrightarrow\left(x-1\right)^3=3^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)

a) \(\left(x+5\right)^2=100\)

=> \(\orbr{\begin{cases}\left(x+5\right)^2=10^2\\\left(x+5\right)^2=\left(-10\right)^2\end{cases}}\)

=> \(\orbr{\begin{cases}x+5=10\\x+5=-10\end{cases}}\)

=> \(\orbr{\begin{cases}x=5\\x=-15\end{cases}}\)

b) \(\left(2x-4\right)^2=0\)

=> \(2x-4=0\)

=> \(2x=4\)

=> \(x=2\)

c) \(\left(x-1\right)^3=27\)

=> \(\left(x-1\right)^3=3^3\)

=> \(x-1=3\)

=> \(x=4\)

1) \(\left(x-3\right)^2-4=0\)

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

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)=0\)

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

2) \(x^2-2x=24\)

\(\Leftrightarrow x^2-2x-24=0\)

\(\Leftrightarrow x^2+4x-6x-24=0\)

\(\Leftrightarrow x\left(x+4\right)-6\left(x+4\right)=0\)

\(\Leftrightarrow\left(x+4\right)\left(x-6\right)=0\)

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

Câu 3 số xấu rồi e