Question

Answer 1

a. $x+5x^2=0$

$\Leftrightarrow x(1+5x)=0$

$\Leftrightarrow x=0$ hoặc $1+5x=0$

$\Leftrightarrow x=0$ hoặc $x=\frac{-1}{5}$

b.

$x+1=(x+1)^2$
$\Leftrightarrow (x+1)^2-(x+1)=0$

$\Leftrightarrow (x+1)[(x+1)-1]=0$

$\Leftrightarrow (x+1)x=0$

$\Leftrightarrow x+1=0$ hoặc $x=0$

$\Leftrightarrow x=-1$ hoặc $x=0$

c.

$x^3+x=0$

$\Leftrightarrow x(x^2+1)=0$

$\Leftrightarrow x=0$ hoặc $x^2+1=0$ 

$\Leftrightarrow x=0$ (chọn) hoặc $x^2=-1<0$ (loại)

Answer 2

h.

$8x^3+12x^2+6x+1=0$

$\Leftrightarrow (2x+1)^3=0$

$\Leftrightarrow 2x+1=0\Leftrightarrow x=\frac{-1}{2}$

i.

$5x(x-1)=x-1$

$\Leftrightarrow 5x(x-1)-(x-1)=0$

$\Leftrightarrow (x-1)(5x-1)=0$

$\Leftrightarrow x-1=0$ hoặc $5x-1=0$

$\Leftrightarrow x=1$ hoặc $x=\frac{1}{5}$

k.

$2(x+5)-x^2-5x=0$
$\Leftrightarrow 2(x+5)-(x^2+5x)=0$

$\Leftrightarrow 2(x+5)-x(x+5)=0$

$\Leftrightarrow (x+5)(2-x)=0$
$\Leftrightarrow x+5=0$ hoặc $2-x=0$

$\Leftrightarrow x=-5$ hoặc $x=2$

Answer 3

d.

$x^3-0,25x=0$

$\Leftrightarrow x(x^2-0,25)=0$

$\Leftrightarrow x(x-0,5)(x+0,5)=0$

$\Leftrightarrow x=0$ hoặc $x-0,5=0$ hoặc $x+0,5=0$

$\Leftrightarrow x=0$ hoặc $x=0,5$ hoặc $x=-0,5$

e.

$x^2-10x=-25$
$\Leftrightarrow x^2-10x+25=0$

$\Leftrightarrow (x-5)^2=0\Leftrightarrow x-5=0$

$\Leftrightarrow x=5$ 

g.

$4x^2-4x=-1$

$\Leftrightarrow 4x^2-4x+1=0$

$\Leftrightarrow (2x-1)^2=0$

$\Leftrightarrow 2x-1=0\Leftrightarrow x=\frac{1}{2}$

Answer 4

h) 8x³ + 12x² + 6x + 1 = 0

(2x)³ + 3.(2x)².1 + 3.2x.1² + 1³ = 0

(2x + 1)³ = 0

2x + 1 = 0

2x = -1

x = -1/2

i) 5x(x - 1) = x - 1

5x(x - 1) - (x - 1) = 0

(x - 1)(5x - 1) = 0

x - 1 = 0 hoặc 5x - 1 = 0

*) x - 1 = 0

x = 1

*) 5x - 1 = 0

5x = 1

x = 1/5

Vậy x = 1/5; x = 1

k) 2(x + 5) - x² - 5x = 0

2(x + 5) - (x² + 5x) = 0

2(x + 5) - x(x + 5) = 0

(x + 5)(2 - x) = 0

x + 5 = 0 hoặc 2 - x = 0

*) x + 5 = 0

x = -5

*) 2 - x = 0

x = 2

Vậy x = -5; x = 2