Question

Tìm x:

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

b) \(3\left(x-3\right)-4x+12=0\)

c) \(x^3-5x=0\)

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

e) \(x^2-9-4\left(x+3\right)=0\)

f) \(2\left(x-2\right)-x^2+4x-4=0\)

Answer 1

a)

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

x² - x + x - 1 = 0

x² - 1 = 0

x² = 1

\(\Rightarrow\) x = \(\pm\)1

b)

3( x - 3) - 4x - 12 = 0

3x - 9 - 4x - 12 = 0

-x - 21 = 0

-x = 21

\(\Rightarrow\)x = -21

c)

x³ - 5x = 0

x( x² - 5) = 0

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x2-5=0\Rightarrow x2=5\Rightarrow x\in\varnothing\end{matrix}\right.\)

\(\Rightarrow\)x = 0

Answer 2

d)

(3x - 2)² - (x + 2)² = 0

9x² - 12x + 4 - x² - 4x - 4 = 0

8x² - 16x = 0

(làm tương tự như c)

e)

x² - 9 - 4(x + 3) = 0

x² - 9 - 4x - 12 = 0

(x² - 4x + 4) - 13 -12 = 0

(x - 2)² - 25 = 0

(x - 2)² = 25

\(\Rightarrow\) x - 2 = 5

\(\Rightarrow\)x = 7

Answer 3

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

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

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

=>x=1 hoặc x=-1

b)3(x-3)-4x+12=0

3(x-3)-4(x-3)=0

(x-3)(3-4)=0

-(x-3)=0

x+3=0

x=3

c)x³-5x=0

x²(x-5)=0

=>x=0 hoặc x=5

d)(3x-2)²-(x+2)²=0

(3x-2-x-2)(3x-2+x+2)=0

(2x-4)4x=0

=>x=2 hoặc x=0

e)=x²-3²-4(x+3)=0

(x-3)(x+3)-4(x+3)=0

(x+3)(x-3-4)=0

(x+3)(x-7)=0

=>x=3 hoặc x=7

f)2(x-2)-x² +4x -4=0

2(x-2)-(x-2)²=0

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

(x-2)(4-x)=0

=>x=2 hoặc x=4