Question

a) 5x(x – 2000) – x + 2000 = 0 b) 5x2 = 13x

c) x3+2x=0                                d) x(x-5)= 5-x

 e) (x+2)2 = x+2                         f) x3 +4x =0

g)3x (x-10) =x-10                     h) x(x+7) =4x+28

Answer 1

a) \(5x\left(x-2000\right)-x+2000=0\)

\(\Leftrightarrow5x\left(x-2000\right)-\left(x-2000\right)=0\)

\(\Leftrightarrow\left(5x-1\right)\left(x-2000\right)=0\)

\(\Leftrightarrow x\in\left\{\frac{1}{5};2000\right\}\)

Answer 2

b) \(5x^2=13x\)

\(\Leftrightarrow x\left(5x-13\right)=0\)

\(\Leftrightarrow x\in\left\{0;\frac{13}{5}\right\}\)

Answer 3

c) \(x^3+2x=0\)

\(\Leftrightarrow x\left(x^2+2\right)=0\)

Vì x^2+2 > 0 nên x = 0

Answer 4

d) \(x\left(x-5\right)=5-x\)

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

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

\(\Leftrightarrow x\in\left\{-1;5\right\}\)

Answer 5

e) \(\left(x+2\right)^2=x+2\)

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

\(\Leftrightarrow x\in\left\{-1;-2\right\}\)

Answer 6

f) \(x^3+4x=0\)

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

Vì x^2+4 > 0 nên x = 0

Answer 7

g) \(3x\left(x-10\right)=x-10\)

\(\Leftrightarrow\left(3x-1\right)\left(x-10\right)=0\)

\(\Leftrightarrow x\in\left\{\frac{1}{3};10\right\}\)

Answer 8

\(x\left(x+7\right)=4x+28\)

\(\Leftrightarrow\left(x-4\right)\left(x+7\right)=0\)

\(\Leftrightarrow x\in\left[4;-7\right]\)